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Chapter 3: Q. 23 (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.

Hint: If necessary, write fin the form f(x)=a(x-h)2+k.

f(x)=x2+4x+2

Short Answer

Expert verified

The required graph is shown below:

Step by step solution

01

Step 1. Write the given function in vertex form.

The given function is:

f(x)=x2+4x+2

Add and subtract the square of half of the coefficient of x.

f(x)=(x2+4x)+2+4-4f(x)=(x2+4x+4)+2-4f(x)=(x+2)2-2

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=-2,k=-2. It means the graph of the given function is a parabola that opens up and has its vertex at (-2,-2)and its axis of symmetry is the line x=-2.

The graph of y=x2shifts 2 units left and 2 units down.

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

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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Most popular questions from this chapter

In problems 3-6, use the figure to solve each inequality.

a) f(x)>0

b)f(x)鈮�0

Match each graph to one the following functions.

f(x)=x2+2x+1

The vertical line passing through the vertex of a parabola is called the ______________.

In Problems 6鈥� 8, graph each quadratic function using transformations (shifting, compressing, stretching, and/or reflecting).

fx=2x+12+4

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.

Hint: If necessary, write fin the form f(x)=a(x-h)2+k.

f(x)=x2-6x-1
See all solutions

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