How do I use the vertex formula to determine the vertex of the graph for y=2x^2 +11x-6?

May 3, 2015

The vertex form of a quadratic is
$y = m {\left(x - \textcolor{red}{a}\right)}^{2} + \textcolor{b l u e}{b}$
when expressed in this form, the vertex is located at
$\left(x , y\right) = \left(a , b\right)$

$y = 2 {x}^{2} + 11 x - 6$

$y = 2 \left({x}^{2} + \frac{11}{2} x\right) - 6 \text{ extracting the "m" value}$

$y = 2 \left({x}^{2} + \frac{11}{2} x + {\left(\frac{11}{4}\right)}^{2} - {\left(\frac{11}{4}\right)}^{2}\right) - 6$ " completing the square"#

$y = 2 \left(x + \left(\frac{11}{4}\right)\right) - \frac{121}{8} - 6$

$y = 2 \left(x - \textcolor{red}{\left(- \frac{11}{4}\right)}\right) + \textcolor{b l u e}{\left(- \frac{169}{8}\right)} \text{ simplifying into vertex form}$

The vertex is at
$\left(x , y\right) = \left(- \frac{11}{4} , - \frac{169}{8}\right)$