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Chapter 9: Q27. (page 594)

Describe how the graph of each function is related to the graph of

f(x)=x2.

f(x)=13x2

Short Answer

Expert verified

The graphf(x)=13x2is the graph vertically compressed from the parent function f(x)=鈥夆赌�x2.

Step by step solution

01

Step 1. State the concept.

Vertical Stretch and Vertical Compression:

y=afx,a>1. Sketch the graph fxvertically by a factor of a.

y=afx,0<a<1. Compress the graph fx vertically by a factor of a.

02

Step 2. Graph each function. 

The graph of the functionsfx=x2 andfx=13x2 is given by:

03

Step 3. State the interpretation of the graph.

The graph of f(x)=ax2stretches or compress the parent graph vertically. Since a=13, the graph of f(x)=13x2is the graph of fx=x2vertically compressed. Compress the graph of fxvertically by a factor of 13.

Therefore, the graph f(x)=13x2 is the graph of vertically compressed from the parent function fx=x2.

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Most popular questions from this chapter

Record your answers on the answer sheet provided by your teacher or on a sheet of paper.

Use the graph of the quadratic equation shown below to answer each question.

A What is the vertex?

B What is they-intercept?

C What is the axis of symmetry?

D What are the roots of the corresponding quadratic equation?

WRITING MATH Explain how to find the axis of symmetry from an equation for a quadratic equation. What other characteristics of the graph can you derive from the equation? Explain.

Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest tenth.

x2鈭�3x鈭�4=0

Use a table of values to graph each equation.

y=x+3

REASONING Provide a counterexample to the following statement. The vertex of a parabola is always the minimum of the graph.
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