Chapter 9: Q24. (page 594)

Describe how the graph of the function $f (x) = x^{2} - 3$ is related to the graph $f (x) = x^{2}$ .

Short Answer

Expert verified

The graph of the parent function is shifted down to 3 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 of $f (x) = x^{2}$ is translated $|c|$ units is down.

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 $f (x) = x^{2} - 3$

Here, $c = - 3$

So, the graph of the parent function is translated 3 units down to form the graph of the function $f (x) = x^{2} - 3$ .

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

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Describe how the graph of the function $f (x) = x^{2} - 3$ 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=x2−3 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

Applied Mathematics

Pure Maths

Discrete Mathematics

Logic and Functions

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Describe how the graph of the functionfx=x2−3 is 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=x2−3 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

Applied Mathematics

Pure Maths

Discrete Mathematics

Logic and Functions

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Describe how the graph of the function $f (x) = x^{2} - 3$ is related to the graph $f (x) = x^{2}$ .