Quadratic Functions

Question 1

Vertex Form

Answer 1

f(x) = a(x-h)² + k

Question 2

Standard Form

Answer 2

f(x) = ax² +bx + c

Question 3

Intercept Form

Answer 3

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

Question 4

Conic Form

Answer 4

y = 1/4p (x-h)² + k
or
x= 1/4p (y-k)² +h

Question 5

What does the +/- mean in
y = +/- a [ +/- b (x-h)² ] + k

Answer 5

Reflection in the x-axis

Question 6

What does a mean in
y = +/- a [ +/- b (x-h)² ] + k

Answer 6

Vertical stretch/shrink

Question 7

How does the vertical stretch/shrink work?

Answer 7

Stretch by 2 -> *2
Shrink by 1/2 -> *1/2

Question 8

What does b mean in
y = +/- a [ +/- b (x-h)² ] + k

Answer 8

Horizontal stretch/shrink

Question 9

What does the (x-h)² mean in
y = +/- a [ +/- b (x-h)² ] + k

Answer 9

Move to the left/right

Question 10

What does k mean in
y = +/- a [ +/- b (x-h)² ] + k

Answer 10

Move up/down

Question 11

How does the horizontal stretch work

Answer 11

by 2 -> *1/2
by 1/2 -> *2

Question 12

(x-h) (x+h)
If it’s neg., move to the…
If it’s pos., move to the…
when using f(x) = a(x-h) +k

Answer 12

Right
Left

Question 13

How to find the vertex of a function (standard form)

Answer 13

Use x=-b/2a and plug a and b into it
Then plug x into the whole equation

Question 14

IS the min/max x or y?

Answer 14

Y

Question 15

How to find the equation of the parabola with the focus and the directrix.

Answer 15

Create a system using
h+p + h-p if directrix is x= d
plug into equation 1/4p(y-k)² +h
or
k+p + k-p if directrix is y=d
Plug into equation
1/4p(x-h)² +k

Question 16

How to find the equation of a parabola with the vertex and the directrix.

Answer 16

Plug the directrix into the formula (y=k-p or x=h-p) to find the p value.
Plug into equation
y=1/4p(x-h)² +k or x=1/4p(y-h)² + k

Question 17

How to find the equation of a parabola with the focus and the vertex.

Answer 17

Plus the value of the focus into the formula (h, k+p or h+p, k) to find the p value.
Plug into equation
1/4p(x-h)² +k

Question 18

What is the vertex for y=1/4p(x-h)² +k

Answer 18

(h, k)

Question 19

What is the focus for y=1/4p(x-h)² +k

Answer 19

(h, k+p)

Question 19

What is the directrix for y=1/4p(x-h)² +k

Answer 19

y= k-p

Question 20

What is the AOS for 1/4p(x-h)² +k

Answer 20

x=h

Question 21

What is the vertex for 1/4p(y-k)² +h

Answer 21

(h,k)

Question 22

Does 1/4p(y-k)² +h open left/right or up/down

Answer 22

Left/right

Question 23

What is the focus for 1/4p(y-k)² +h

Answer 23

(h+p, k)

Question 24

What is the directrix for 1/4p(y-k)² +h

Answer 24

x= h-p

Question 25

What is the AOS for 1/4p(y-k)² +h

Answer 25

y=k