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Q25.

Expert-verified

Algebra 1

Found in: Page 594

Book edition Student Edition

Author(s) Carter, Cuevas, Day, Holiday, Luchin

Pages 801 pages

ISBN 9780078884801

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Short Answer

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

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

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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.

Most popular questions for Math Textbooks

Which is an equation for the function shown in the graph?

A $y = - 2 x^{2}$

B $y = 2 x^{2} + 1$

C $y = x^{2} - 1$

D $y = - 2 x^{2} + 1$

State whether the given sentence is true or false. If false, replace the underlined term to make a true sentence.

The graph of the parent function is translated down to form the graph $f (x) = x^{2} + 5$ .

Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest tenth.

$- x^{2} + 3 x - 1 = 0$

OPEN ENDED Write a quadratic function for which the graph has an axis of symmetry $x = - \frac{3}{8}$ . Summarize your steps.

Consider $y = x^{2} - 5 x + 4$

Write the equation of the axis of symmetry.

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