# How do you find the vertex of a parabola y=2x^2 -12x+23?

Jul 8, 2015

The easiest way is (probably) to convert the given equation into vertex form.
The vertex is at $\left(3 , 5\right)$

#### Explanation:

Vertex form of a parabola is
$\textcolor{w h i t e}{\text{XXXX}}$$y = m {\left(x - a\right)}^{2} + b$ with its vertex as $\left(a , b\right)$

$y = 2 {x}^{2} - 12 x + 23$
$\textcolor{w h i t e}{\text{XXXX}}$extract the $m$
$y = 2 \left({x}^{2} - 6 x\right) + 23$
$\textcolor{w h i t e}{\text{XXXX}}$complete the square
$y = 2 \left({x}^{2} - 6 x + 9\right) + 23 - 2 \left(9\right)$
$\textcolor{w h i t e}{\text{XXXX}}$simplify into vertex form
$y = 2 {\left(x - 3\right)}^{2} + 5$

Since this is in vertex form, we can read the vertex directly from the equation as $\left(3 , 5\right)$