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Chapter 9: Q. 337 (page 964)

In the following exercises,

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

Part (b): graph it by using transformations.

fx=-x2-4x+2

Short Answer

Expert verified

Part (a): The required function is fx=-x+22+6.

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+2

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

localid="1645121473247" fx=-x2+4x+2fx=-x2+4x+4+2+4fx=-x2+4x+22+6fx=-x+22+6

02

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

Identify the constants,

a=-1,h=-2,k=6

Consider the function fx=x2.

Multiply y-values by -1,

fx=-x2

Shift left by 2units,

fx=-x+22

Shift up by 6units,

fx=-x+22+6

Plot the graph,

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