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Chapter 9: Q. 9.113 (page 953)

Graph f(x)=(x+2)2-3using transformations.

Short Answer

Expert verified

The graph of f(x)=(x+2)2-3is

Step by step solution

01

Step 1. Given data  

The given quadratic function isf(x)=(x+2)2-3

02

Step 2. Determine the horizontal and vertical shift

Comparer the function with f(x)=(x-h)2+k and determine hand k

f(x)=(x+2)2-3f(x)=(x-h)2+ksoh=-2k=-3

So 2units horizontal left shift of f(x)=x2will give

f(x)=(x-2)2

3units vertical downward shift off(x)=(x+2)2will givef(x)=(x+2)2-3

03

Step 3. plot the graph  of the parent function

Plot the graph off(x)=x2

04

Step 4. horizontal shift of the graph

Shift the graph of f(x)=x2to 2units left to plot f(x)=(x+2)2

05

Step 5. vertical shift of the graph

Shift the graph of f(x)=(x+2)2to 3units downward to plot f(x)=(x+2)2-3

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