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Chapter 9: Q. 341 (page 964)

In the following exercise, fx=2x2-4x+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=2x-12-1.

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

Step by step solution

01

Part (a) Step 1. Given information.

Consider the given function,

fx=2x2-4x+1

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

fx=2x2-2x+1fx=2x2-2x+1+1-2fx=2x-12-1

02

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

Identify the constants,

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

Consider the functionfx=x2.

Multiply y-values by 2,

fx=2x2

Shift right 1unit,

fx=2x-12

Shift down 1unit,

fx=2x-12-1

Plot the graph,

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