Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

Q68.

Expert-verified

Algebra 1

Found in: Page 534

Book edition Student Edition

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

Pages 801 pages

ISBN 9780078884801

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

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

A quadratic function for which the graph has an axis of symmetry $x = - \frac{3}{8}$ may be $y = 4 x^{2} + 3 x + 2$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Axis of symmetry.

Write the general form of the axis of symmetry.

The general form of the axis of symmetry is given by $x = - \frac{b}{2 a}$ .

Step 2. Compare.

Compare the general form of the axis of symmetry to the given expression and write the values of a and b.

$- \frac{b}{2 a} = - \frac{3}{8} = - \frac{3}{2 \cdot 4}$

Therefore, $a = 4$ and $b = 3$ .

Step 3. Write the quadratic function.

The standard form of a quadratic function is given by $y = a x^{2} + b x + c$ . Substitute the obtained values of a b and any value of c in the standard form.

$y = 4 x^{2} + 3 x + 2$

Step 4. Summarize steps.

To find the quadratic function from the axis of symmetry,

First, compare a general form of the axis of symmetry to the given expression and write the values of a and b.

Then substitute the obtained values of a,b, and any value of c into the standard form of a quadratic function to find the required quadratic function.

Most popular questions for Math Textbooks

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

Determine whether each trinomial is a perfect square trinomial. Write yes or no. If so, factor it.

$x^{2} + 5 x + 25$

Write a formula that can be used to find the perimeter of a figure containing $n$ squares.

REASONING The graph of a quadratic function has a vertex at $(2, 0)$ . One point on the graph is $(5, 9)$ . Find another point on the graph. Explain how you find it.

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

The solutions of a quadratic equation are called roots.

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free