# What is the vertex form of y=4x^2-13x-6?

Aug 13, 2017

$y = 4 {\left(x - \frac{13}{8}\right)}^{2} - \frac{265}{16}$

#### Explanation:

$y = 4 {x}^{2} - 13 x - 6$

$= 4 \left({x}^{2} - \frac{13}{4} x \textcolor{w h i t e}{\text{XXXXXX}}\right) - 6$

$\frac{1}{2} \cdot \frac{13}{4} = \frac{13}{8}$ and ${\left(\frac{13}{8}\right)}^{2} = \frac{169}{64}$

So inside the parentheses add $\frac{169}{64}$

Outside the parentheses subtract $4 \cdot \frac{169}{64} = \frac{169}{16}$

$y = 4 \left({x}^{2} - \frac{13}{4} + \frac{169}{64}\right) - \frac{169}{16} - \frac{96}{16}$

To finish, factor the expression in parentheses and simplify the subtraction outside the parentheses.

$y = 4 {\left(x - \frac{13}{8}\right)}^{2} - \frac{265}{16}$