Step $1$

First, determine the vertex from the graph.

Step $2$

A quadratic function in standard form is given by the following equation.

$f(x)=a(x-h{)}^2+k$

The vertex $(h,k)$ can be used to fill in the blanks below.

$\{\begin{array}{c}\text{:}f(x)=a(x+33{)}^2-4vv\\ 4\end{array}$

Step $3$

Finally, determine $a.$ The parabola passes through the point $(0,5).$ Substitute the values of $x$ and $y$ into the equation.

$55=a(0+33{)}^2-4$

Solve for $a.$ Simplify the coefficient of a and move all constant terms to the left side of the equation.

$9=(9)a$

Simplify.

$a=121$ Amazing job!

Step $4$

We can now write the equation in standard form. Use $y$ in place of $f(x).$

Modify your answer to the correct form.