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Chapter 9: Q23. (page 594)

Describe how the graph of the function fx=x2+8is related to the graph fx=x2.

Short Answer

Expert verified

The graph of the parent function is shifted up to 8 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 fx=x2 is translated c units down.

03

Step 3. Determine the relationship of the graph of the function fx=x2+8 with the graph of the function fx=x2.

Observe the functionfx=x2+8

Here,c=8

So, the graph of the parent function is translated 8 units up to form the graph of the function fx=x2+5.

Therefore, the graph of the parent function is shifted to 8 units.

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Most popular questions from this chapter

Write an expression for the area of the rectangle below.

F10b5c5鈭�3bcG10b5c5鈭�15b2c3H2b5c5鈭�3b2c3J10b4c6鈭�15bc2

Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.

2x2+x鈭�15=0

Graph the function.

y=鈭�2x2鈭�8x+2

Use a table of values to graph the following functions. State the domain and range.

y=x2+2x+5

Consider y=x2鈭�5x+4

Find the coordinates of the vertex. Is it a maximum or minimum point?
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