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Chapter 9: Q. 338 (page 964)

In the following exercise,fx=-x2+4x-5,

Part (a): rewrite the function infx=ax-h2+kform.

Part (b): graph it by using transformations.

Short Answer

Expert verified

Part (a): The required function is fx=-x+22-1.

Part (b): The required graph is given below,

Step by step solution

01

Part (a) Step 1. Given information.

Consider the given function,

fx=-x2+4x-5

Rewrite the function infx=ax-h2+kform by completing the square,

localid="1645109224843" fx=-x2-4x-5fx=-x2-4x+4-5+4fx=-x-22-1

02

Part (b) Step 1. Graph the function using transformation.

Identify the constants,

a=-1,h=2,k=-1

Consider the function fx=x2.

Multiply y-values by -1,

fx=-x2

Shift right2units,

localid="1645109184684" fx=-x-22

Shift down 1unit,

localid="1645109191908" fx=-x-22-1

Plot the graph,

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