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1
Q

A relation is a function if:

A

It pass the two test:
VLT or for every x- coordinate their is only one y-coordinate

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2
Q

What is domain?

A

Values of all the x- coordinate

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3
Q

What is range?

A

Values of all the y- coordinate

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4
Q

How can you tell apart a linear, quadratic, and exponential?

A

linear: first difference are the same
quadratic: second difference are the same
exponential: difference aren’t the same ex. 2 with a little x.

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5
Q

What is function notation?

A

It’s substituting f of x, and then solving

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6
Q

In y = a ( x-h)2 +k
what is “a”

A

If a is positive: open up
if a is negative it open down, and reflects into the x- axis
if a is a whole number it has a vertical stretch (narrower)
if it a faction or decimal it a compression ( wider)

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7
Q

In y= a (x-h)2 + k
what is h

A

if h is positive: shifts right
if h is negative: shifts left

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8
Q

In y= a (x-h)2 + k
what is k

A

if k is positive it shifts up
if k is negative it shifts down

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9
Q

what is the mother of all parabolas?

A

y=x2

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10
Q

How do you foil?

A

first, outside, inside, last
( x + 4) (2x-9)

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11
Q

how do you common factor?

A

Find the GCF
dived all number by
the GCF goes outside the bracket, and the dived number go inside.

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12
Q

how do you do simple trinomials

A

find the GCF
then do the chart method find the two numbers that multiply by a and c, but add to b
then put those number in the bracket

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13
Q

How do you know if it’s simple or complex trinomials?

A

simple their GCF is the first number “a”
complex find another GCF or do the chart method

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14
Q

in y= a (x-r) (x-s)
what is a

A

if a is positive the graph open up if it’s negative it open down
if a is > 1 it stretches’
if 0< a> a it compressed

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15
Q

in y= a( x-r) (x-s)
what is r and s?

A

r and s are the zeros

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16
Q

how do you find the zeros in an equation from standard from?

A

fully factor
then replace y for 0
and you switch the sign of the number

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17
Q

how do you find the difference of the square?

A

common factor if need be
you square root each factor
then plug it in
(x-6) (x+6)

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18
Q

how do you find the perfect square?

A

keep the sign
square root the a and c term
and plug it in with a exponent
(x-4)2 check it by multiply 2(4) (x) = the b term

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19
Q

what is the optimal value

A

is the value of the y- co-ordinate of the vertex

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20
Q

what is the axis of symmetry

A

divides the the parabola into two equal halfs

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21
Q

what the discriminant

A

b2 - 4 a c

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22
Q

how many roots are their if the discriminant is positive, negative or equal

A

positive= 2
negative= 0
equal= 1

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23
Q

how do you use the discriminant to find the roots?

A

plug into your equation

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24
Q

when do you use the whole discriminant formula?

A

when your looking for zeros, and the number are tricky like decimal

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25
In application of quadratics how do you find the height?
you plug in 0 as you x in your equation and then you solve
26
In application of quadratics how do you find when something is going to hit the ground?
your looking for the zeros so factor if needed then plug in zeros and change the signs.
27
In application of quadratics how do you find the max/ min height?
add your zeros and dived by 2 this get you your x value the plug that number into your equation
28
how do you solve by graphing?
this is used for standard form Use the formula x= -b/ 2(a) this find you the x of your vertex then plug that x into your equation to get y of your vertex then make a t chart, and plug in the x to find your y graph find your solution
29
when creating an equation from graphs for factor form what do you need?
y= a (x-s) (x-r) x= inter y= inter plug in to solve for "a"
30
when creating an equation from graphs for vertex form what do you need?
y= a (x-h) 2 +k vertex y= inter plug in to solve for "a"
31
how do you complete the square?
stander to vertex remove a from the first two terms then find b/2 exponent 2 plug in that number as positive and negative find the square root of a and the positive now plug those number (x+3) 2 -9 multiply the negative by the outside number then add by the out out side number to get you equation.
32
what can you find with Vertex form? y= a ( x-h) 2 +k
Vertex: can be found (h,k) y= inter: plug in 0 to solve axis: is h optimal value: k x- inter: hard to find you have to factor first
33
what can you find with factored form? a(x-s) (x-r)
x- inter: switch the sign of s and r vertex: add the x's and then dived by 2: (x,?) then sub to solve for for y of the vertex y= inter: plug in 0 to slove axis: x optimal: y
34
what can you find with standard form? ax2 + bx+ c
y= inter: plug in 0 to solve vertex: must compete the square x- inter: factor first axis symmetry/ optimal value: factoring, x= -b/ 2(a) or complete the square
35
how do you get from standard to vertex, and the opposite?
standard to vertex: factoring vertex to standard: foil
36
how do you get from standard to factoring, and the opposite?
standard to factoring: completing the square factoring to standard: foil
37
how do you get from factoring to vertex, and the opposite?
factoring to vertex: graphing vertex to factoring: solve for "a"
38
where does the hyp, opp, and adj go on right triangle?
hyp: is the longest side adj: has the right angle, and the angle opp: is opposite from the angle
39
when solving for the unknowns tan 30= X/ 10 what do you do?
you add 10 to both sides then solve 10 tan 30
40
when solving for the unknowns cos 52= 20/ x what do you do?
add y to both side y cos 52= 30 dived the one side by the cos 52 y= 30/ cos 52 dived to solve
41
when solving for the unknowns sin x = 5/12 what do you do?
do the sign inverse -1 sin (5/12) plug it in to solve
42
what the angle of elevation?
the angle looking up
43
what the angle of depression?
the angle looking down
44
what the one thing to remeber with the angle of depression and elevation
it makes the z pattern
45
in sine law how do you solve sin 93/ x+= sin 55/ 17
you change the dominator dived the both sides by number with x to get x
46
in sine law how do you solve for an angle?
you change the dominator dived both sides by that number to sine inverse to get an angle
47
in cosine law how do you find SAS?
use the formula cos < = c2-a2-b2/ -2 a b Then you should get a fraction to do the invers
48
in cosine law how do you find the SSS?
use the formula c2= a2+b2-2 ab cos < solve get a positive number and the square root
49
what is peak?
the highest point on the graph
50
what is trough?
the lowest point on the graph
51
how do you know if it's periodic?
there a repeating pattern
52
what is period?
the horizontal length of one cycle on the graph
53
what the amp?, and how do you find it?
half the distance between the max and min max - min/ 2
54
what is period of a sine function?
period is 360
55
what is equation of axis and how do you find it?
half the distance horizontally add the max and min and divide by 2
56
what is the sin function formula?
a sin ( x +<) + d
57
how do you graph -2 sin ( x + 180 degrees) -1
1. sin x 2. strech by -2 so multiply each y by -2 3. reflection in x-axis 4. shift left by 180 degrees so move the point over left 180 5. shift down by 1
58
what is the sin x
- 360, 0 -270, 1 -180, 0 -90, -1 0, 0 90, 1 180, 0 270, -1 360, 0
59
what the multiplication rule?
add the exponent if the base is the same
60
what the division rule?
subtract the exponent if the base is the same
61
what the power of power?
multiply the 2 exponent 6 3) 5 3x5+= 15 6 15
62
what the zero exponent rule?
a0= 1
63
how do you do fraction exponents?
the exponent goes on both the numerator and the dominator
64
how do you do the negative exponents?
if there a negative exponent you have to flip the number so it's a positive , and then solve
65
how do you do the rational exponents?
if their a one as the numerator you put into the calculator as the denomator square root the number if there a another number on top you put the bottom number and the square root to the exponent of the top number
66
In y= a. b x what does it mean
a= y= inter b= ratio
67
what does an exponential graph have?
1. they never touch the asymptote 2. they have y-inter 3. if the b is greater than 1 it increasing if between 0- 1 it's decreasing =1 : horizonatl line 4. if there a constant ratio
68
what happen when the b value is greater
the graphs becomes greater
69
what the ratio?
it the number the y are multiply by
70
what is the doubling time?
it's the time it takes for a population to double in size P= Po (2) t/d
71
what is the population of growth or decay?
The population for growth means it's increasing P= P0 ( 1+r) n The population for decay means it's decreasing P= P0 ( 1-r)n
72
what is the half-life?
the half life is the time it takes for a quantity to decay to half it's original amount.
73
What is simple interest?
I= prt FV= p+ I It's simple so their no compounding periods or monthly payment
74
what is Fv compound interest?
Fv= p ( 1 + r) t I= fv-p it has compounding periods, but no monthly payments. it in the future so later
75
What is FV annuity?
Fv= R x (1 + i) n- 1/ i it has compounding periods, monthly payments, and is in the future so later
76
what PV annuity?
PV= R x( 1-( 1+i)-n/ i it has compounding periods, monthly payments, and is present so right now
77
what the annually compounding period?
1
78
what the semi- annually compounding period?
2
79
what the quarterly compounding period?
4
80
what the monthly compounding period?
12
81
what the daily compounding period?
356
82
what an amortization schedule?
a record of payment showing the interest paid, the principal, the current balance on a loan or investment
83
what the PV in compound interest?
Pv = fv/ ( 1+ r) n it has compounding periods, but no monthly payment. it the present so right now
84
In y= a sin ( x- <) + d what is a
if a is multiply by a number between 0 and 1 it compress if it multiply by a number greater than 1 will compress if there a negative it reflection into x- axis
85
In y= a sin ( x- <) + d what is <
that the degrees by adding it shift left by subtracting it shift right
86
In y= a sin ( x- <) + d what is d
by adding it shift up by subtracting it shift down

Math (7 decks)

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