# What is the vertex form of 2y=5x^2+8x − 4.?

Jun 25, 2017

The vertex form is $y = \frac{5}{2} {\left(x + \frac{4}{5}\right)}^{2} - \frac{18}{5}$

#### Explanation:

Let simplify the equation by completing the squares

$2 y = 5 {x}^{2} + 8 x - 4$

Dividing by $2$

$y = \frac{5}{2} {x}^{2} + 4 x - 2$

$= \frac{5}{2} \left({x}^{2} + \frac{8}{5} x\right) - 2$

Completing the squares, adding half of the coefficient of $x$ to the square and removing it

$y = \frac{5}{2} \left({x}^{2} + \frac{8}{5} x + {4}^{2} / {5}^{2}\right) - 2 - \frac{5}{2} \cdot {4}^{2} / {5}^{2}$

$y = \frac{5}{2} \left({x}^{2} + \frac{8}{5} x + \frac{16}{25}\right) - 2 - \frac{8}{5}$

Factorising

$y = \frac{5}{2} {\left(x + \frac{4}{5}\right)}^{2} - \frac{18}{5}$

This is the vertex form

graph{y=5/2(x+4/5)^2-18/5 [-8.89, 8.89, -4.444, 4.445]}