Chapter 9: Q23. (page 594)

Describe how the graph of the function $f (x) = x^{2} + 8$ is related to the graph $f (x) = x^{2}$ .

Short Answer

Expert verified

The graph of the parent function is shifted up to 8 units.

Step by step solution

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

A quadratic function, which is written in the form, $y = a x^{2} + b x + c$ , where, $a \neq 0$ is called the standard form of the quadratic function.

Step 2. Define vertical translation of the graph.

The graph $g (x) = x^{2} + c$ is the graph $f (x) = x^{2}$ translated vertically.

If $c > 0$ , the graph $f (x) = x^{2}$ is translated $|c|$ units up.

If $c < 0$ , the graph $f (x) = x^{2}$ is translated $|c|$ units down.

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

Observe the function $f (x) = x^{2} + 8$

Here, $c = 8$

So, the graph of the parent function is translated 8 units up to form the graph of the function $f (x) = x^{2} + 5$ .

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

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Describe how the graph of the function $f (x) = x^{2} + 8$ is related to the graph $f (x) = x^{2}$ .

Short Answer

Step by step solution

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

Step 2. Define vertical translation of the graph.

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

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

Short Answer

Step by step solution

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

Step 2. Define vertical translation of the graph.

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Mechanics Maths

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

Describe how the graph of the function $f (x) = x^{2} + 8$ is related to the graph $f (x) = x^{2}$ .