# How do you write f(x)=2x^2-7x-4 in vertex form?

Aug 14, 2016

$y = 2 {\left(x - \frac{7}{4}\right)}^{2} - \frac{81}{8}$

#### Explanation:

Given -

$y = 2 {x}^{2} - 7 x - 4$

Find the vertex $\left(x , y\right)$

$x = \frac{- b}{2 a} = \frac{- \left(- 7\right)}{2 \times 2} = \frac{7}{4}$

At $x = \frac{7}{4}$

$y = 2 {\left(\frac{7}{4}\right)}^{2} - 7 \left(\frac{7}{4}\right) - 4 = - \frac{81}{8}$

$x , y$ coordinates of the vertex are $\left(\frac{7}{4} , - \frac{81}{4}\right)$

The vertex form of the quadratic equation is -

$y = a {\left(x - h\right)}^{2} + k$

We need the values of $a , h , k$

$a = 2$ [coefficient of ${x}^{2}$]
$h = \frac{7}{4}$ [x-coordinate of the vertex]
$k = \frac{- 81}{8}$[ y-coordinate of the vertex]

Now plug in the values in the equation

$y = 2 {\left(x - \frac{7}{4}\right)}^{2} - \frac{81}{8}$