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Chapter 9: Q24. (page 594)

Describe how the graph of the functionfx=x2鈭�3 is related to the graph fx=x2.

Short Answer

Expert verified

The graph of the parent function is shifted down to 3 units.

Step by step solution

01

Step 1. Define the standard form of the quadratic function.

A quadratic function, which is written in the form, y=ax2+bx+c, where,a鈮�0 is called the standard form of the quadratic function.

02

Step 2. Define vertical translation of the graph.

The graph gx=x2+c is the graph fx=x2 translated vertically.

If c>0, the graph fx=x2 is translated c units up.

If c<0, the graph of fx=x2 is translated c units is down.

03

Step 3. Determine the relationship of the graph of the function fx=x2−3 with the graph of the function fx=x2.

Observe the function fx=x2鈭�3

Here,c=鈭�3

So, the graph of the parent function is translated 3 units down to form the graph of the function fx=x2鈭�3.

Therefore, the graph of the parent function is shifted down to 3 units.

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Most popular questions from this chapter

State whether the given sentence is true or false. If false, replace the underlined term to make a true sentence.

The solutions of a quadratic equation are called roots.

OPEN ENDED Write a quadratic function for which the graph has an axis of symmetry x=鈭�38. Summarize your steps.

Use a table of values to graph the given equation. State the domain and range.

y=2x2鈭�4x+3

MULTIPLE REPRESENTATIONS in this problem, you will investigate solving quadratic equations using tables.

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d. VERBAL Compare the signs of the function values for x values just before and just after a zero. What happens to the sign of the function value before and after a zero?

State whether the given sentence is true or false. If false, replace the underlined term to make a true sentence.

The graph of a quadratic function has a maximum if the coefficient of the x2is positive.
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