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Q68.

Expert-verifiedFound in: Page 534

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 $\mathit{y}\mathbf{=}\mathbf{4}{x}^{2}+\mathbf{3}x+\mathbf{2}$.

Write the general form of the axis of symmetry.

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

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 $b=3$.

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.

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

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.

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