# What is the vertex of  y= 2x^2+5x-13-4(x-1)^2?

Mar 3, 2018

The vertex is $\left(\frac{13}{4} , \frac{33}{8}\right)$.

#### Explanation:

We expand and combine like terms:
$y = 2 {x}^{2} - 4 {x}^{2} + 5 x + 8 x - 13 - 4 = - 2 {x}^{2} + 13 x - 17$
The x-coordinate of the vertex is:
$x = - \setminus \frac{b}{2 a} = \frac{13}{4} = 3 \frac{1}{4}$
$y = \frac{33}{8} = 4 \frac{1}{8}$
Therefore, the vertex is $\left(\frac{13}{4} , \frac{33}{8}\right)$.