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Chapter 9: Q. 330 (page 964)

In the following exercises, (a) rewrite each function in f(x)=a(x-h)2+kform and (b) graph it by using transformations.

f(x)=x2+4x-12

Short Answer

Expert verified

The function in the form f(x)=a(x-h)2+kis

f(x)=(x+2)2-16and the graph is

Step by step solution

01

Given information

Given equation,f(x)=x2+4x-12

02

Rewriting and completing the square

Rewriting, we get

f(x)=x2+4x-12f(x)=x2+2.2.x+22-12-22f(x)=x2+4x+4-16f(x)=(x+2)2-16

03

Calculate the parameters

Calculating, we get

f(x)=(x+2)2-16a=1(h,k)=(-2,-16)

The parabola opens upward and axis of symmetry isx=-2

Theyintercept isrole="math" localid="1645157028522" f(0)=(0+2)2-16f(0)=-12

04

Sketching the graph

The graph is shift of f(x)=x2 to the left by two units and vertically downward by sixteen units

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