Chapter 9: Q17. (page 566)

Describe how the graph of the given function is related to the graph of $f (x) = x^{2}$
$g (x) = x^{2} - 6$

Short Answer

Expert verified

The graph of $g (x) = x^{2} - 6$ is the graph of $f (x) = x^{2}$ , vertically translated 6 units down.

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 the transformations of the graph of the function.

(1) The graph of $f (x) + c$ shifts the graph of $f (x), c$ units up.

(2) The graph of $f (x) + c$ shifts the graph of $f (x), c$ units down.

Step 3. Describe how the graph of gx=x2−6 is related to the graph of fx=x2.

Observe the equation $g (x) = x^{2} - 6$ .

The constant term $c$ is $- 16$ , so the graph is translated 6 units down.

Therefore, the graph of $g (x) = x^{2} - 6$ is the graph of $f (x) = x^{2}$ , vertically translated 6 units down.

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Describe how the graph of the given function is related to the graph of $f (x) = x^{2}$
$g (x) = x^{2} - 6$

Short Answer

Step by step solution

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

Step 2. Define the transformations of the graph of the function.

Step 3. Describe how the graph of gx=x2−6 is related to the graph of fx=x2.

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Describe how the graph of the given function is related to the graph of fx=x2gx=x2−6

Short Answer

Step by step solution

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

Step 2. Define the transformations of the graph of the function.

Step 3. Describe how the graph of gx=x2−6 is related to the graph of fx=x2.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Probability and Statistics

Decision Maths

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Describe how the graph of the given function is related to the graph of $f (x) = x^{2}$
$g (x) = x^{2} - 6$