Q68. - Algebra 1

Question

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

Step-by-Step Solution

Answer

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

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.

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

 

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.

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

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.