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Chapter 9: Q. 518 (page 987)

In the following exercises, write the function in fx=ax-h2+kform:

Short Answer

Expert verified

The equation isf(x)=x-22+4.

Step by step solution

01

Step 1. Given information. 

We have graph given below:

02

Step 2. Find the function using vertex form. 

Notice that the graph have a vertex of 2,4and passes through 4,8and 0,8.

The vertex form is given by:

f(x)=ax-h2+k

For -2,4:

y=f(x)=ax-(2)2+4y=a(x-2)2+4

Note that the graph passes through the point 0,8.

So, substitute x=0and y=8:

8=a(0-2)2+4 a=1

Substitute a=1in the vertex form:

f(x)=1x-22+4f(x)=x-22+4

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