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Expert-verified Found in: Page 534 ### Algebra 1

Book edition Student Edition
Author(s) Carter, Cuevas, Day, Holiday, Luchin
Pages 801 pages
ISBN 9780078884801 # 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 $\mathbit{y}\mathbf{=}\mathbf{4}{x}^{2}+\mathbf{3}x+\mathbf{2}$.

See the step by step solution

## 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 $x=-\frac{b}{2a}$.

## Step 2. Compare.

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

$-\frac{b}{2a}=-\frac{3}{8}\phantom{\rule{0ex}{0ex}}=-\frac{3}{2\cdot 4}$

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

## Step 3. Write the quadratic function.

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

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

## 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. ### Want to see more solutions like these? 