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Chapter 9: Q10. (page 597)

Describe how the graph of each function is related to the graphf(x)=x2.

h(x)=12x2+4

Short Answer

Expert verified

The graph h(x)=12x2+4is the graph role="math" localid="1647861887784" f(x)=鈥夆赌�x2 vertically compressed by a factor 12 and shifted up 4 4units.

Step by step solution

01

Step 1. State the concept.

Vertical Stretch and Vertical Compression:

y=af(x),a>1. Sketch the graphf(x)vertically by a factor of a.

y=af(x),0<a<1. Compress the graphf(x)vertically by a factor of a.

02

Step 2. Graph each function. 

The graph of the functionsf(x)=x2andh(x)=12x2+4is given by:

03

Step 3. State the interpretation of the graph.

The function can be written asf(x)=ax2+c, wherea=12andc=4.

Note: When cis positive, the graph of a function is translated up and if cis negative, the graph of the function is translated down.

Since0<a<1andcis positive, the graph h(x)=12x2+4is the graphf(x)=x2vertically compressed by a factor12and shifted up 4 units.

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