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

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.

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

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.

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

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.