# What is the vertex of  y=2x^2 -12x+23?

Apr 7, 2017

$\left(3 , 5\right)$

#### Explanation:

The equation of a parabola in $\textcolor{b l u e}{\text{vertex form}}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a {\left(x - h\right)}^{2} + k} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where (h ,k) are the coordinates of the vertex and a is a constant.

$\text{Rearrange " y=2x^2-12x+23" into this form}$

$\text{Using the method of " color(blue)"completing the square}$

$y = 2 \left({x}^{2} - 6 x + \frac{23}{2}\right)$

$\textcolor{w h i t e}{y} = 2 \left(\left({x}^{2} - 6 x \textcolor{red}{+ 9}\right) \textcolor{red}{- 9} + \frac{23}{2}\right)$

$\textcolor{w h i t e}{y} = 2 \left({\left(x - 3\right)}^{2} + \frac{5}{2}\right)$

$\textcolor{w h i t e}{y} = 2 {\left(x - 3\right)}^{2} + 5 \leftarrow \textcolor{red}{\text{ in vertex form}}$

$\text{here " h=3" and } k = 5$

$\Rightarrow \text{vertex} = \left(3 , 5\right)$
graph{2x^2-12x+23 [-16.02, 16.02, -8.01, 8.01]}