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Chapter 9: Q. 344 (page 964)

In the following exercise,fx=-3x2+6x+1,

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

Part (b): graph it by using transformations.

Short Answer

Expert verified

Part (a): The required function is fx=-3x-12+4.

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

Step by step solution

01

Part (a) Step 1. Given information.

Consider the given function,

fx=-3x2+6x+1

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

localid="1645118443327" fx=-3x2-2x+1fx=-3x2-2x+1+1+3fx=-3x-12+4

02

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

Identify the constants,

a=-3,h=1,k=4

Consider the function fx=x2.

Multiply y-values by -3,

fx=-3x2

Shift right by 1unit,

fx=-3x-12

Shift up by 4units,

fx=-3x-12+4

Plot the graph,

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