Chapter 9: Q25. (page 594)

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

Short Answer

Expert verified

The graph of the parent function is vertically stretched by a factor of 2.

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.

The graph $k f (x)$ will vertically stretch the graph $f (x)$ by a factor $k$ if $k > 1$ and will vertically compress the graph $f (x)$ by a factor $k$ if $0 < k < 1$ .

Step 3. Determine the relationship of the graph of the function fx=2x2 with the graph of the function fx=x2.

Observe the equation $f (x) = 2 x^{2}$ .

The graph is multiplied by $k = 2$ , so the graph is vertically stretched by a factor of 2.

Therefore, the graph of the parent function is vertically stretched by a factor of 2.

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Describe how the graph of the function $f (x) = 2 x^{2}$ 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 the transformations of the graph of the function.

Step 3. Determine the relationship of the graph of the function fx=2x2 with the graph of the function fx=x2.

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Describe how the graph of the function fx=2x2is 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 the transformations of the graph of the function.

Step 3. Determine the relationship of the graph of the function fx=2x2 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

Mechanics Maths

Calculus

Discrete Mathematics

Pure Maths

Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.

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