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Flashcards in 3 DECK SCRAMBLE Deck (284)
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1

what is a coefficient?

the number in front of a variable or variables

2

f(x) = ax^2 + bx + c What is the coefficient of the linear term?

b

3

f(x)= 2(x+4)^2-3 What is vertex and which way does it open?

at (-4, -3) and it opens upwards (has min)

4

why are roots called "zeros"

because it is where the height is zero; where the y value is zero; they are the x values that make the y=0

5

What is the x intercept of a line? (what are the coordinates?)

Where the line crosses the horizontal axis, the x axis. The coordinates are ( X, 0 )

6

how do you find "probability"

experimental: (#successes)/(total # tries).
theoretical: (# successful outcomes) / (# total possible outcomes)

7

When are there no solutions to simultaneous equations?

when the lines don't cross, when they are parallel (no overlap)

8

When completing the square and "a" is not equal to 1, what do you have to do?

divide both sides of equation (every term) by that "a" to turn "a" into "1"

9

f(x)= -2(x-5)^2- 3What is vertex and is it a min or a max? What is the axis of symmetry?

at ( 5, -3) and it is a maximum, the AOS is x=5

10

what is the constant term's exponent on the x?

0

11

How do you get the probability of taking a certain route on a tree diagram?

multiply the branches along the path till the end. write it at the end of the branch.

12

How can you tell if the point (5, -3) is a solution to a linear equation?

If it "works." Sub 5 in for the X and -3 in for the Y. Simplify. If the statement is true, then it is a solution. If it is a solution, then it is on the line.

13

When is there and infinite number of solutions to simultaneous equations?

when they are the same line, then all points on the line satisfy both equations

14

one out of four is _____ or ____%

0.25 or 25%

15

three out of five is ____ or ____%

0.6 or 60%

16

f(x)= 5 - 2x +3x^2 What is a, b and c ?

a = 3, b = -2, c = 5

17

What are the fractional equivalents of these popular decimals:
0.5 , 0.333, 0.25, 0.2, 0.125, 0.1, 0.01, 0.001

1/2, 1/3, 1/4, 1/5, 1/8, 1/10, 1/100, 1/1000

18

change the probability of 3/5 to a decimal and a percent

0.6 or 60%

19

What is the zero product property?

(this)(that)=0 is true when (this)=0 and when (that)=0. this is what we use when solving by factoring.

20

change the probability 40% to a decimal

0.4

21

Explain what a parabola with two real roots (real zeros) looks like.

crosses x axis at those roots, at those x values

22

How do you solve by isolating the x^2 ? (when can you do it?)

When there is no linear term (no x term), simply act like you're solving for x, but solve for x2 and in the last step, take square root of both sides ( + / - )

23

change the probability 0.5 to a percent

50%

24

What do we call b^2-4ac

the discriminant

25

can you have more than 100% of something?

YES.... if you have more than a whole. (but this can't be a probability)

26

what are the decimal equivalents of these popular fractions:
1/2, 1/3, 1/4, 1/5, 1/8, 1/10, 1/100, 1/1000

0.5 , 0.333, 0.25, 0.2, 0.125, 0.1, 0.01, 0.001

27

change the decimal 0.0003 to a percent

0.03%

28

What are the roots of a function? (other names?)

the zeros, the x-intercepts, the solutions,where the parabola crosses

29

f(x) = ax^2 + bx + c What is the constant term?

c (it is the y intercept)

30

If an x intercept is 455, what point is on the line?

(455, 0)

31

what does a slope that is undefined look like?

vertical, straight up and down. The y axis has a slope of zero.

32

why is it called a constant term

alone it would be a constant function.. The same height always. a horizontal line with a constant y, a constant height

33

What is the standard form of a quadratic?

ax2+bx+c = 0

34

How many diamonds in a deck of cards?

13

35

what is the quadratic term's exponent on the x ?

2

36

f(x)= 3x^2-6x+3 What is the constant term? what is the y intercept?

3, it is the also the y intercept

37

Why can't you divide by zero? (why can zero be in the top and not the bottom?)

10/2 asks "how many times do you add 2 to itself to get to 10?" the answer is 5.
10/0 asks "how many times do you add 0 to istelf to get to 10?" the answer is there is no answer. undefined

38

where is the vertex located?

on the axis of symmetry (highest or lowest point).

39

What are the three forms of a quadratic that we use?

standard: y = ax2-bx-c
factored: y = a (x-r) (x-r)
vertex: a (x-h)2 +k

40

How can you always get rid of fractions in any equation?

Multiply every term by the LCD (plop the LCD in the numerators, then simplify)

41

What is the gradient of a vertical line?

undefined

42

change the probability 0.04 to a percent

4%

43

one out of three is ____ or ____%

about .33 or 33%

44

how would you solve (3x-2)(x-5)=0 (what are solutions?)

set factors = 0 and solve: 3x-2=0 and solve x-5=0 zero product property. The solutions are x = { 5, 2/3}

45

what is tricky about the vertex form?

the -h part.. If its (x+9)2 +8 then h is -9.. remember that x=h is also the AOS !!!

46

What if you solve simultaneous equations all three ways, what will you notice?

they all give the same answer, the same POINT, (x,y)

47

If the discriminant is zero, what do you know about roots?

there is one double root, it is a perfect square, the parabola just touches down x axis without crossing, the vertex is on the x axis.

48

if there are 10 kids and you are choosing 3 to bring on a trip, how many ways can you do that? (perm or comb?)

Combination. nCr with n=10 and r=3

49

How do you show that a point lies on a line?

Show that, when you plug the point in, you get a true mathematical statement.

50

What are the solutions of a function? (other names)

the roots, the x intercepts, the zeros where the parabola crosses

51

How do you find the vertex of a parabola in standard form? y=ax^2+bx+c

the x value is always -b/2a . To get the y value for it, put that x value into the function and solve

52

what is the tough thing about quadratics?

the fact that they are squared.. We have to undo that x2. We want to get it linear!!

53

What does (A')' look like when shading?

double negative. (A')' = A, so the entire A circle should be shaded.

54

What is the x coordinate for all y-intercepts?

zero. all y intercepts are in the middle, not left or right, because they are on the y axis.

55

How do you solve by factoring?

get stuff all on one side, factor, set each factor = 0, solve each linear equation.

56

f(x) = a(x-h)^2 + k where it the vertex? what is the Axis of Symmetry?

vertex at the point (h, k), the AOS is the vertical line x= h

57

When you shade a VENN diagram, what does A U B look like?

Both circles and the overlap are all shaded (everything inside)

58

Perpendicular lines have _____ gradients, or slopes

OPPOSITE SIGN AND RECIPROCAL

59

How do you convert from vertex to standard form?

square the binomial and combine stuff

60

What does the discriminant tell us about?

about the roots, the zeros, how many x intercepts the parabola has, how many times it crosses the x axis, whether roots are real or imaginary

61

change the probability of 2/3 to a decimal and a percent

about .67 or 67% (.66666666666)

62

What is the "general" form of a line?

Ax + By = C no fractions.

63

what is the "most popular" form of a line?

gradient intercept (slope intercept)

64

What does the quadratic formula say about finding the x intercepts? (stand where and do what?)

stand at the AOS and reach up and down a bit to find the solutions

65

Geometrically, how is the shape of a parabola made?

A parabola is the set of all points equidistant from point, called the focus, and a line, called the directrix.

66

How many kings in a deck of cards?

4

67

Describe what an axis of symmetry is

it is where the parabola can fold onto itself. It is the equation of this vertical line, so you write "x = ___"(-b/2a)

68

f(x) = a(x-h)^2 + k How do we know if it opens up or down?

by the sign of a, if its positive, up, negative , down

69

what is the slope of a line that goes straight up and down?

undefined

70

when you are given a two way table, what should you always do?

PUT IN THE TOTALS ON SIDE and BOTTOM and the OVERALL TOTAL IN THE CORNER

71

what is the probability of getting 3 tails in a row flipping a coin?

1/2 x 1/2 x 1/2 = 1/8

72

one out of ten is _____ or ____%

0.1 or 10%

73

What are the zeros of y=5(x-3)(2x+1)

The zeros, or roots, or x intercepts are at(3, 0) and (-1/2, 0)

74

What is the discriminant?

b2-4ac (notice there is no sq root on it!!)

75

If the discriminant is zero, how many times does the parabola hit the x axis?

1. hits it and bounces off.

76

How is the axis of symmetry hidden in the quadratic formula?

it is the beginning.. (put both parts over 2a).. -b/2a

77

What is the quadratic formula?

x = -b +- sqroot b squared - 4ac all over 2a (but in formula)

78

f(x)= 3x^2-6x+3 What is the coefficient of the linear term?

-6 this is also known as "b"

79

What is the gradient-intercept form?

y = mx + c

80

f(x)= 3x^2-6x+3 What is the linear term?

-6x

81

what is the linear term's exponent on the x ?

1

82

change the probability of 1/4 to a decimal and a percent

0.25 or 25%

83

What is the gradient of a horizontal line?

ZERO

84

How do you solve simultaneous equations by substitution?

isolate a variable. SUBSTITUTE into the other equation, solve, then sub back in to find (x,y)

85

What is the symbol that joins two sets together into one set?

A big U , stands for UNION

86

how can you think of 150% of something?

150% of a pizza is one and a half pizzas!! (this can't be a probability)

87

What numbers can represent a probability?

Always between 0 and 1, examples: 0, .75, .05, 1, .35

88

change the decimal 0.03 to a fraction

3/100

89

f(x)= -4x^2 + 8 What is a, b and c ?

a = -4, b = 0, c = 8

90

What does A' mean?

The elements not in A

91

how would you solve 4x^2 - 9 = 13 ? (just say what you'd do)

no linear term, so just isolate the x2 and root sides

92

What is the probability of randomly taking one card and getting a diamond from a deck?

13/52 or 1/4

93

f(x) = ax^2 + bx + c What is the coefficient of the constant term?

c (it is the y intercept)

94

change the decimal 0.0003 to a fraction

3/10000

95

What is the y intercept of a line? (what are the coordinates?)

Where the line crosses the vertical axis, the y axis. The coordinates are ( 0, Y )

96

What is a midpoint?

the point halfway along a segment. right in the MIDDLE

97

f(x)= -4x^2 + 8 What is the axis of symmetry?

x= -b/2a = -0/2(-4) = 0/8 = 0. AOS is x=0, which is the y axis!!

98

change the probability of 1/3 to a decimal and a percent

about .33 or 33% (.33333333333)

99

If the discriminant is negative, what do you know about roots?

there are no real roots, 2 imaginary roots, the parabola doesn't touch x axis

100

change the probability of 1/2 to a decimal and a percent

0.5 or 50%

101

How do you find the midpoint between two given points?

the midpoint has an x and y value, (x,y). the X value is the average of the two x values, and the Y value is the average of the two y values.

102

change the probability of 2/5 to a decimal and a percent

0.4 or 40%

103

How would you solve 9x^2 - 3x = 0 ? (just say what you'd do)

factor out x and set factors=0.. (one solution will be 0)

104

What is a perpendicular bisector?

the line that goes through the midpoint of a segment, and it is also perpendicular to it.

105

Explain what the graph of a parabola with no real roots (real zeros) looks like.

doesn't touch x axis

106

If a line as a slope of -5, then any line parallel to it will have a slope of ___ and any line perpendicular to it will have a slope of ___

-5 and perp 1/5

107

why is it called a discriminant?

because it discriminates between which type of solutions, roots and zeros you will have (2real, one real or imaginary)

108

What are the zeros of a function? (other names?)

the roots, the x intercepts, the solutions, where the parabola crosses

109

When is there just one solution to simultaneous equations?

when they cross (at one point)

110

How can you think of %

PER 100 (or, divided by 100)

111

What are the five ways to solve a quadratic?

set to zero and factor, complete square, quadratic formula, graph and look for x-intercepts, or when there is no linear term, isolate the x2 and root both sides.

112

What is the graph of a line showing us? (or a graph of a parabola or any function)

It is showing us all of the points, (x,y), that make the equation true. Every dot on the graphed line will make the equation true, they all work.

113

What is the slope of a line in standard (general) form?

-A/B

114

Are all quadratics similar?

YES.. THEY ALL HAVE THE EXACT SAME SHAPE.. They are simply zoom-ins or zoom-outs of eachother..

115

thinking of the quadratic formula, why are there no real roots when you have a negative discriminant?

because you have to take the square root of a negative, which is an imaginary number. You end with an imaginary number.. .hence.. Imaginary roots (not real)

116

How do you find the average of two numbers?

add them up and divide by 2

117

change the decimal 0.03 to a percent

3%

118

If A = { 1, 2 }, how many elements does A have?

two

119

When you graph a line or a parabola, what are you actually graphing?

THE SOLUTION! Those are all of the points that make the equation true. All of the points that "work". If you put any other pionts, (x,y) into the equation, they wont work, You will get a false statement.

120

What do students forget about OR ?

The OR BOTH part. The union of A and B are all of the elements in A, in B and also the ones that are in BOTH.

121

If we are given an x, like x=5, and need to fine a y that goes with it, how do we find it?

substitute the 5 in for the x in the eqution and solve for y, That y value goes with the 5. The point (5, y) will be on the line.

122

How can you tell if the point (5, -3) is on a line or a parabola if you are given the equation?

If it "works." Sub 5 in for the X and -3 in for the Y. Simplify. If the statement is true, then it is a solution. If it is a solution, then it is on the line.

123

Why do parabolas look different if they are all similar?

Well.... Simply either imagine zooming way in or zooming way out... this method can always get any 2 parabolas to look the same.

124

If A = { 1, 2, 6} , what is n(A) ?

n(A) is the number of elements in A. In this case, n(A)= 3

125

where is the combination button on the calculator?

Math > PRB then down to nCr

126

What is the gradient formula? (the slope formula?)

m = ( y - y ) / ( x - x )

127

AND goes with ______ [union or intersection]

intersection

128

change the probability of 1/5 to a decimal and a percent

0.2 or 20%

129

What is solution to:5(x-8)(x+3)=0

8 and -3.
(this)(that)=0 situation
this=0 and that=0
we are looking for the x values that make the equation true.. so we want to make x-8=0 and x+3=0

130

Why is it called "gradient-intercept" form? (slope-intercept)

There is a gradient and a slope explicitly shown in the formula

131

three out of ten is ____ or ____%

0.3 or 30%

132

If the discriminant is positive, how many times does the parabola hit the x axis?

2

133

How do you graph a quadratic in standard form?
f(x)=ax^2+bx+c

first graph the Axis of symmetry with dotted line, (x= -b/2a) then make a T table and use that x value to find the vertex and use a couple integers near it to find other points. LEAVE SPACE FOR ARITHMETIC. Reflect over the AOS and connect the dots

134

what are the coordinates of a point?

(x,y), the x and y value.

135

What is a slightly different form of the general form you may be asked to write an equation in?

Ax + By + D = 0 in stead of Ax + By = C

136

What are the fractional equivalents of these popular percents:
50%, 33.3%, 25%, 20%, 12.5%, 10%, 1%, 0.1%

1/2, 1/3, 1/4, 1/5, 1/8, 1/10, 1/100, 1/1000

137

If you have 3 pairs of shoes, two pairs of pants and 4 shirts.. how many outfits?

3*2*4= 24 outfits

138

INTERSECTION goes with _____ [OR or AND]

AND

139

If you are given two points and need to find the equation of a line, how do you do it?

First, fine the gradient using m=(y-y)/(x-x), then use that gradient and EITHER OF THE POINTS. Put it in point gradient form. (point slope form)

140

How do you know when a parabola is smiling?

when a is positive

141

What are the x intercepts of: y=5(x+6)(x-3)

at -6 and at 3(they are also called solutions or zeros)

142

If a y intercept is 990, what point is on the line?

(0, 990)

143

If the discriminant is positive, what do you know about roots?

there are 2 real roots, and the parabola crosses x axis twice..at these roots

144

change the decimal 0.3 to a percent

30%

145

f(x)= -4(x-8)^2+6What is vertex and which way does it open?
what is AOS?

at (8, 6) and opens downward (has max). The AOS is x=8

146

the number 5/0 is equal to :

undefined

147

How many cards in a deck of cards?

52

148

What is solution to:g (x+f)(x-w) = 0

-f and w(this)(that)=0 situationthis=0 and that=0we want to make equation trueso we solve x+f=0 and x-w=0

149

With two simultaneous linear equations, what are the three options for a solution?

No solution, one solution, or an infinite number of solutions.

150

What does (A U B)' look like when shading?

shade just the area outside of the circles.

151

How do you find the max or min value of a quadratic in either form?

it is the y value at the vertex. In vertex form, it's simply k. In standard form, Plug -b/2a into the function to get y.remember to look at "a" + smiles have min.. - frowns have max. OR PUT IN YOUR CALCULATOR AND USE MAX MIN FINDER.

152

If you know that a quadratic has x intercepts at 5 and 3, , what is the factored form?
What is the equation of AOS?

factored form: y = a (x-3)(x-5)
aos: x=4
notice aos is average of 3 and 5
(3+5)/2 = 4

153

two out of five is ____ or ____ %

0.4 or 40%

154

How do you know when it is a quadratic?

when the highest degreed term is the x^2 term (quadrus:square)

155

what completes the square and what is the factored form? x2 + 6x + ____

9 completes it and the factored form is (x+3)^2

156

What is the probability of randomly picking one card a red card from a deck?

26/52 or 1/2

157

What is the gradient of a flat (horizontal) surface?

ZERO

158

How do you solve simultaneous equations by elimination?

organize equations so they line up nice. Get coefficients to be opposites. Add equations and solve. Then sub back in to find (x,y)

159

On a number line, what is the midpoint between 8 and 12?

at the average: 10. 10 is halfway between 8 and 12. add and divide by 2. 8+12=20. 20/2= 10

160

change the probability 0.8 to a percent and a fraction

80% and 4/5

161

What are the decimal equivalences of these popular percents?
50%, 33.3%, 25%, 20%, 12.5%, 10%, 1%, 0.1%

0.5 , 0.333, 0.25, 0.2, 0.125, 0.1, 0.01, 0.001

162

Parallel lines have ______ gradients, or slopes

the same

163

change the decimal 0.003 to a fraction

3/1000

164

two out of three is ____ or ____%

about .667 or 66.7%

165

If the discriminant is negative, how many times does the parabola hit the x axis?

0

166

If there are 10 kids and you are choosing a president, vp and treasurer, how many ways can you do that? (perm or comb)

Permutation. nPr with n=10 and r=3

167

How do you solve simultaneous equations by graphing?
(what if they are quadratics?)

graph both lines and look for the intersection, the solution is the coordinates (x,y) If they are quadratics they could have 2 intersections.

168

Why does AND go with INTERSECTION? A ∩ B = A and B

Because you have to be a member of both A and a member of B to be a part of A ∩ B

169

f(x)= 3x - 9 What is a, b and c?

a = 0 , b = 3, c = -9..There is no quadratic term..
THIS IS LINEAR!!!
IT'S A LINE!
slope of 3

170

What is the solution to simultaneous equations? (system of equations?)

The set of points that satisfies (makes true) all of the equations in the system. In algebra 1, this is just ONE POINT, (x,y), But we will solve quadratic-linear systems that will have 2 solutions.

171

change the probability of 1/10 to a decimal and a percent

0.1 or 10%

172

What are the x intercepts of a function? (other names?)

the roots, the zeros, the solutions

173

What fractions can represent a probability?

Any fraction as long as the top is smaller than the bottom (or equal). IT CAN'T BE TOP HEAVY!

174

When can you just isolate the x^2 and root both sides?

when there are no linear terms (only quad and const)

175

What is the symbol that just takes the overlap of two sets?

An upside down U, look like this: ∩, INTERSECTION

176

f(x) = ax^2 + bx + c What is the linear term?

bx (the term is the whole thing)

177

thinking of the quadratic formula, why are there 2 real roots when the discriminant is positive?

because there is a square root of a positive, you will have to + and - that in the top, giving 2 different real solutions.

178

What are the gradients (slopes) of the diagonals of a square?

+1 going up L to R, and -1 going down from L to ROW

179

f(x)= 6x^2- 7x What is a, b and c ?

a = 6, b=-7, c = 0

180

What is a way to help shading in VENN diagrams?

Label the areas 1, 2, 3 and 4. Let A= {1,2} B= {2,3} , intersection is {2} and outside of the circles {4).

181

f(x)= (x+9)^2-8 What is vertex and is it a min or a max?

at (-9, -8) and it is a minimum

182

How could simultaneous quadratic equations have no solutions?

two parabolas curving away from eachother and never crossing is one possibility.

183

Does "a" have to be equal to 1 when completing a square?

YES

184

if you know that the x intercepts of a parabola are at (-3, 0) and (9,0), what is the factored form and what is AOS?

factored form: y= a (x+3) (x-9)
aos at x = (-3+9) / 2 = 6/2
aos at x=3

185

What are simultaneous equations? (system of equations)

a group of equations

186

f(x)= 3x^2-6x+3 What is the coefficient of the constant term?

3 this is also known as "c"

187

What is the probability of randomly taking one card and getting a king from a deck?

4/52 or 1/13

188

f(x)= 3x^2-6x+3 What is the quadratic term?

3x^2

189

what is point-gradient form? (point slope)

A rearrangement of the gradient formula: y-y =m (x-x)

190

How can centimeters and a meter stick help you think of percent?

Think of centimeters as "PERCENTIMETERS".. each one is one percent of a meter. 35cm is 35% of a meter.

191

What are the three ways we solve simultaneous equations?

Graphing (and looking for intersection), substitution and elimination

192

How do you know when a parabola is frowning?

when a is negative

193

change the probability 0.5% to a decimal

0.005

194

How could simultaneous equations have exactly two solutions?

Imagine a line and a parabola. the line could cross the parabola twice.

195

What is an interesting fact about slopes between -1 and +1?

HALF OF ALL POSSIBLE SLOPES ARE BETWEEN -1 and +1 (and they are perpendicular)

196

When we graph a parabola to solve a quadratic, what do we look for?

look for the x intercepts, these are the roots. The zeros, the solutions

197

If a line as a slope of 2/3, then any line parallel to it will have a slope of ___ and any line perpendicular to it will have a slope of ___

2/3 and perp -3/2

198

If there is no constant term, what is an easy way to factor?

just factor out the x and set the factors to zero (one solution is zero)

199

four out of five is ____ or ____%

0.8 or 80%

200

why are they called "quadratics?"

from latin "quadrus" which means SQUARE

201

What do the probabilities on the branches leaving a single node in a tree diagram have to add to?

1. If you have two branches, then they should add to 1, if you have five branches from same node, all five added together should equal 1.

202

When you shade a VENN diagram, what does A ∩ B look like?

Just the overlap sliver in the middle is shaded.

203

With tree diagrams, what does MA.AD stand for?

Multiply across, Add down

204

What is the equation of the y axis?

x=0

205

If we are given a Y value, like y-8, and need to find the x that goes with it, how do you do it?

substitute the 8 in for the y in the equation and solve for x. That x goes with the 8. the point (x, 8) will be on the line.

206

What are solutions to (x+8)(x-3) = 0

x = { -8, 3} this is not a point on the graph, it is a set of two numbers that make the equation true. They are also the x intercepts of the parabola

207

can you have a probability of 5/3?

NO... that is more than 1

208

What does it mean to "satisfy" an equation?

Make the equation true.

209

What are the three forms of a quadratic function?

Standard y=ax^2+bx+c
Vertex y=a(x-h)^2+k
Factored y= a(x-r)(x-r)

210

What is the eqution of a horizontal line that goes through the y axis at 8?
How can you think about it to help you?

y = 8. Since y is the height, you can think of it as all of the points that have a height of 8. Also, you can think of it as all of the points that have a y value of 8, so you are a solution if your y value is 8.

211

Why is it called "point-gradient" form?

There is a point and a gradient explicitly shown in the form

212

f(x)= 6x^2- 5x What is the axis of symmetry?

x= -b/2a = -(-5)/2(6) = 5/12, AOS x= 5/12

213

How do you find the equation of a perpendicular bisector?

Find the point and the gradient (slope) and put it in point-gradient form. The point is the midpoint (use averages) and the slope is the RECIPROCAL and OPPOSITE of the slope between the two given points.

214

can you have a probability of 3/5?

Yes, that's 60%

215

thinking of the quadratic formula, why is there only one real root when the discriminant is zero?

because the square root of zero is zero, so you are going to + and - zero... the quad formula reduces to -b/2a .. The only root is the axis of symmetry (the vertex is on the x axis)

216

change the probability of 0.45 to a percent

45%

217

change the probability 0.04% to a decimal

0.0004

218

How do we handle that squared term? how can we undo it?

by either splitting the x's apart by factoring, or by taking a square root somewhere..

219

What is the equation of the axis of symmetry?

x = -b / 2a
x= opposite b / twice a
(notice it is the equation of a vertical line)

220

Does "a" have to be equal to 1 when doing quadratic formula?

NO

221

How do you know if a parabola in standard form opens upward (smile) or down (frown)?

if "a" is pos it opens up. if a is negative, it opens down. Positive people smile, negative people frown.

222

change the probability 0.0003 to a percent

0.03%

223

can you have a probability of 0.5?

Yes, that's 50%

224

How do a lot of people think about the gradient
(the slope)?

rise/run... or change in y / change in x

225

Can you have a probability of 3.5?

NO. probabilities are between 0 and 1

226

change the probability of 3/4 to a decimal and a percent

0.75 or 75%

227

What is probability?

The likelihood of an event happening.

228

can you have a percent of 5/4 ?

YES! that would be 125%..... (this can't be a probability)

229

one out of five is ____ or ____%

0.20 or 20%

230

change the decimal 0.003 to a percent

0.30%

231

Explain what a parabola with one real root (real zero) looks like.

just touches x axis at one spot, the root (the zero), it doesn't cross it, it bounces off it, called a "double root", the vertex is on the x axis

232

How do you know if a parabola has a max or minimum by looking at the function in standard form?

if " a" is pos, it has a min. if 'a' is negative, it has a max

233

what completes the square and what is the factored form? x^2 - 8x + ____

16 completes it and the factored form is (x-4)^2

234

f(x) = a(x-h)^2 + k
How do we know if it has max or min?
what is the AOS?

by the sign of a, if its positive it opens up so it has a MIN, negative it opens down so it has a MAX.
aos at x=h

235

change the probability of 4/5 to a decimal and a percent

0.8 or 80%

236

How do you solve by completing the square?

get all quadratic and linear term on one side and bring constant term over to other.... Make sure a=1, take half of b and square it, add it to both sides. Factor, root, solve

237

what does a slope of zero look like?

horizontal, flat from left to right. The x axis has a slope of zero.

238

What is the gradient of a line?

the slope, the steepness

239

UNION goes with ______ [OR or AND]

OR

240

What is the the difference between theoretical and experimental probability?

theoretical is from thinking of all of the possibilities and doing it with math, experimental is the #successes/total attempts you observe.

241

Why is it called a "linear" term

alone its graph would be a straight line

242

What is the y coordinate for all x-intercepts?

zero. all x intercepts have a height of zero because they are on the x axis.

243

the number 0/5 is equal to :

zero. 0

244

Do all quadratic functions have x intercepts?

No, some don't touch the x axis.. These have imaginary roots and a negative discriminant

245

Difference between a Permutation and a Combination?

Permutation is choosing and Placing in a Particular Place, Combinations are just choosing

246

what is difference between (3, -2) and {3, -2}

the first is a point on a plane (over 3, down 2) and is in parentheses... The second set are numbers in braces, so it is simply a set containing two values, 3 and -2. It is not a point on a plane, the order does non matter in braces.

247

What is the midpoint of (4, 5) and (6, 15). (think, the average of 4 and 6, and the average of 5 and 15

average of 4 and 6 is 5. the average of 5 and 15 is 10. so at (5, 10)

248

f(x) = ax^2 + bx + c What is the coefficient of the quadratic term?

a

249

What is the equation of the x axis?

y = 0
all horizontal lines are in the form y=something

250

What is a solution to an equation?

A solution is the set of values that makes an equation TRUE.

251

How can you find the x intercepts from an equation of a line?

Plug zero in for Y, and solve for X. The coordinates will be ( X, 0)

252

How can you find the y intercepts from an equation of a line?

Plug zero in for X and solve for Y. The coordinates wll be (0, Y)

253

Why does OR go with UNION, ex. A U B = A or B

Because you are part of the union as long as you are a part of A or B or BOTH

254

f(x)= 3x^2-4x+5 What is a, b and c ?

a = 3, b = -4, c = 5

255

change the probability 5% to a fraction

1/20 (one out of 20)

256

change the decimal 0.3 to a fraction

3/10

257

The three forms of equations of a line we use are :

point-gradient form, gradient-intercept form, general form

258

f(x) = ax^2 + bx + c What is the quadratic term?

ax2

259

f(x)= 3x2-6x+3 What is the axis of symmetry?

-b/2a = -(-6)/2(3) = 6/6 = 1

260

What is the vertex form of a quadratic?

f(x) = a(x-h)^2 + k

261

If there is no linear term, what is an easy way to solve?

simply isolate the x^2 and root both sides.

262

OR goes with______ [union or intersection]

union

263

one out of twenty is ____ or _____%

0.05 or 5%

264

How can you think of a slope of 1 or -1?

A perfect diagonal of a square, 45 degrees!

265

change the probability of 1/8 to a decimal and a percent

0.125 or 12.5%

266

In general, what are we looking for with two simultaneous linear equations?

THE INTERSECTION! (X, Y) ! the intersection is the solution, it is the point that makes both equations true, it satisfies both equations.

267

What is the equation of a vertical line that goes through the x axis at 7?
How can you think of that line to help make sense of it?

x = 7. You can think all of the points that are over 7 to the right.. or "all of the points on this line have an x value of 7, so you are a solution as long as your x=7.

268

where is the permutation button on the calculator?

Math > PRB then down to nPr

269

Do all quadratics have a y intercept

YES... All quadratics have exactly 1 y-intercept.. (c).. if there is no constant term, the y intercept is 0, so the parabola passes through the origin!!!!

270

f(x)= 3x^2-6x+3 What is the coefficient of the quadratic term?

3 this is also known as "a"
notice that 3x^2 is the entire quadratic term, 3 is just he coefficient.

271

change the probability of 6% to a decimal

0.06

272

How can you always find the y intercept of a line?

plug zero in for x and find the y. y intercept at (0, y)

273

how can you always find the x intercept of a funciton

plug zero in for y and find the x or x's. x intercept at (x,0)

274

what are the three forms of a linear equation?`

standard (general): Ax + By + C = 0
slope (gradient) intercept: y = mx + b
point - slope (gradient): y-y = m (x-x)

275

How can you use calculator to find aos?

Graph the parabola, then use MAX or MIN. the x value is the AOS.

276

What is a cool feature you can use when tracing along a graph on your calculator?

While tracing, you can type any x value and it will give you the y value for that x , and hence, the coordinates (x,y)

277

what does the line y=x look like?

an uphill diagonal of a square. It goes from bottom right to top left.

278

what does the line y= - x look like?

A downhill diagonal of a square. It goes from top left to bottom right.

279

What does line y= -4 look like?

a HORIZONTAL (left to right) line through y=-4. It is below the x axis. All of the points on the line have a y value of -4.

280

What does the line x = 8 look like?

a VERTICAL line (up and down) through x = 8. it is to the right of the y axis. All of the points on the line have an x value of 8.

281

what is the equation of the x axis?

y = 0 (all of the points on x axis have a y value of zero)

282

what is the equation of the y axis?

x = 0 (all of the points on the y axis have an x value of zero)

283

what does y=0 look like?

It is the x axis. all of the points on x axis have a y value of zero.

284

what does x=0 look like?

It is the y axis. All of the points on the y axis have an x value of zero.