quadratics

Question 1

What is the vertex form of a quadratic?

Answer 1

f(x)=a(x-h)²+k

Question 2

What is the standard form of a quadratic?

Answer 2

f(x)=ax²+bx+c

Question 3

What is the factored form of the quadratic?

Answer 3

f(x)=a(x-p)(x-q)

Question 4

What do h and k stand for in the vertex form?

Answer 4

(h,k) is the vertex

Question 5

What do p and q stand for in the factored form of a quadratic?

Answer 5

x intercepts

Question 6

What are the x intercepts from f(x)=2(x-3)(x+4)

Answer 6

(3,0) (-4,0)

Question 7

What are the x intercepts from f(x)=(2x-3)(x-1)

Answer 7

(1,0) (3/2,0)

Question 8

What are the x intercepts from f(x)=2x(x-7)

Answer 8

(0,0) (7,0)

Question 9

What are the x intercepts from f(x)=(x+1)(x-2)

Answer 9

(-1,0) (2,0)

Question 10

What does c stand for in standard form?

Answer 10

y intercept

Question 11

What does a tell you in quadratic equations?

Answer 11

if it opens up or down, if it skinny or fat

Question 12

If a is negative, will the graph open up or down?

Answer 12

down

Question 13

If a is positive, will the graph open up or down?

Answer 13

up

Question 14

Give the a, b, c values of the following f(x)=2x²-3x+4

Answer 14

a= 2 b= -3 c=4

Question 15

Give the vertex from the following equation f(x)=2(x+3)²+4

Answer 15

(-3,4)

Question 16

When we see (x-3)^2 how do we distribute the 2?

Answer 16

foil

Question 17

What is the first thing to look for when factoring

Answer 17

greatest common factor

Question 18

When a>1 how do we start to factor?

Answer 18

multiply a and c

Question 19

To factor when a=1, do the numbers multiply to b or c?

Answer 19

c

Question 20

To factor when a=1, do the numbers add to b or c?

Answer 20

b

Question 21

How do you write equations for axis of symmetry

Answer 21

x=

Question 22

How do you find the axis of symmetry from standard form?

Answer 22

x= -b/2a

Question 23

How do you find the axis of symmetry from factored form?

Answer 23

(p+q)/2

Question 24

How do you find the axis of symmetry from vertex form?

Answer 24

h

Question 25

What are the two ways we can find the x intercepts from standard form of a quadratic?

Answer 25

quadratic equation, factoring

Question 26

How do you get from factored form to x intercepts?

Answer 26

set each ( ) = 0 and solve for x

Question 27

Zero product property

Answer 27

If two things are multiplied together to equal 0, one of the multiplied terms must equal 0

Question 28

What is the quadratic equation?

Answer 28

Question 29

What form must the equation be in to use the quadratic equation?

Answer 29

standard

Question 30

How do we get x intercepts from vertex form?

Answer 30

set y=0 and solve for x

Question 31

If we get a square root of a negative number, what does that mean?

Answer 31

imaginary x intercepts

Question 32

If asked for roots what are you finding

Answer 32

x intercepts

Question 33

If asked for zeros what are you finding?

Answer 33

x intercepts

Question 34

If asked for the solutions of ab equation when y=0 what are you finding?

Answer 34

x intercepts

Question 35

What is the x value of the vertex?

Answer 35

axis of symmetry

Question 36

How do you find the y value of the vertex

Answer 36

plug axis of symmetry in for x in the equation

Question 37

if a is positive will the vertex be a maximum or minimum?

Answer 37

min

Question 38

if a is negative will the vertex be a maximum or minimum?

Answer 38

max

Question 39

What buttons do you press on the calculatorm after you put in the equation to find the max/min

Answer 39

2nd Trace

Question 40

Where do you put the cursor when the bottom of teh screen says left bound?

Answer 40

to the left of the max/min

Question 41

Where do you put the cursor when the bottom of teh screen says right bound?

Answer 41

to the right of the max/min

Question 42

What are the 5 key points needed to graph a quadratic?

Answer 42

y intercept, mirror of y intercept, vertex, 2 x intercept (if any)

Question 43

Points mirror across what in a quadratic function?

Answer 43

axis of symmetry

Question 44

if you are mirroring the y intercept, what will the value of the mirrored point be?

Answer 44

the same as the y intercept

Question 45

How do you find the x value of a mirrored point

Answer 45

The mirrored point is the same distance from the axis of symmetry as the original point

Question 46

What is the discriminant?

Answer 46

b²-4ac

Question 47

If there are 2 real x intercepts, what do you know about the discriminant?

Answer 47

discriminant\>0

Question 48

If there are 0 real x intercepts, what do you know about the discriminant?

Answer 48

discriminant\<0

Question 49

If there are 2 real repeating x intercepts, what do you know about the discriminant?

Answer 49

discriminant=0

Question 50

If there is 1 x intercept, what do you know about the discriminant?

Answer 50

discriminant=0

Question 51

If the discriminant is\<0 what will the graph look like?

Answer 51

The parabola will not cross the x axis

Question 52

If the discriminant =0 what will the graph look like?

Answer 52

The parabola will touch the x axis, but not cross the x axis

Question 53

If the discriminant =0 what do you know about the vertex?

Answer 53

The vertex is the x intercept