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Chapter 9: Q 340 (page 964)

In the following exercise,f(x)=3x2+18x+20,

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

Part (b): graph it by using transformations.

Short Answer

Expert verified

Part (a): The required function is fx=3x+32-7.

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

Step by step solution

01

Part (a) Step 1. Given information.

Consider the given function,

f(x)=3x2+18x+20

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

fx=3x2+6x+20fx=3x2+6x+9+20-27fx=3x+32-7

02

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

Identify the constants,

a=3,h=-3k=-7

Consider the function fx=x2.

Multiply y-values by 3,

fx=3x2

Shift left 3units,

localid="1645112176321" fx=3x+32

Shift down 7units,

localid="1645112184357" fx=3x+32-7

Plot the graph,

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