Finding the Vertex of a Quadratic Function

$\begin{array}{c}\text{The horizontal coordinate of the vertex will be at}\hfill \\ & \hfill h& =& -\frac{b}{2a}\hfill \\ & & =& -\frac{\mathrm{-6}}{2(2)}\hfill \\ & & =& \frac{6}{4}\hfill \\ & & =& \frac{3}{2}\hfill \\ \text{The vertical coordinate of the vertex will be at}\hfill \\ & \hfill k& =& f(h)\hfill \\ & & =& f\left(\frac{3}{2}\right)\hfill \\ & & =& 2{\left(\frac{3}{2}\right)}^2-6\left(\frac{3}{2}\right)+7\hfill \\ & & =& \frac{5}{2}\hfill \end{array}$

Rewriting into standard form, the stretch factor will be the same as the $a$ in the original quadratic. First, find the horizontal coordinate of the vertex. Then find the vertical coordinate of the vertex. Substitute the values into standard form, using the " $a$ " from the general form.

The standard form of a quadratic function prior to writing the function then becomes the following: