Question

Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it.

Answer 1

Answer:

Step-by-step explanation:

f

(

x

)

=

−

4

(

x

−

8

)

2

+

3

Set the polynomial equal to  

y

to find the properties of the parabola.

y

=

−

4

(

x

−

8

)

2

+

3

Use the vertex form,  

y

=

a

(

x

−

h

)

2

+

k

, to determine the values of  

a

,  

h

, and  

k

.

a

=

−

4

h

=

8

k

=

3

Since the value of  

a

is negative, the parabola opens down.

Opens Down

Find the vertex  

(

h

,

k

)

.

(

8

,

3

)

Find  

p

, the distance from the vertex to the focus.

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−

1

16

Find the focus.

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(

8

,

47

16

)

Find the axis of symmetry by finding the line that passes through the vertex and the focus.

x

=

8

image of graph