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Chapter 3: Q. 22 (page 156)

Graph the function fby starting with the graph of y=x2and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

f(x)=(x-3)2-10

Short Answer

Expert verified

The required graph is shown below:

Step by step solution

01

Step 1. Given information.

The given function is:

f(x)=(x-3)2-10

02

Step 2. Determine the transformations used.

In the function f(x)=a(x-h)2+k,ais a constant and (h,k)is the vertex.

In the given function a=1,h=3,k=-10. It means the graph of the given function is a parabola that opens up and has its vertex at (3,-10)and its axis of symmetry is the line x=3.

The graph of y=x2shifts 3 units right and 10 units down.

First plot the graph of y=x2then shift it 3 units right and then shift the resulted graph 10 units down to get the graph of the function f(x)=(x-3)2-10.

03

Step 3. Draw the graph.

The required graph is shown below:

Using a graphing utility, we get a graph that is the same as the above graph.

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