# What is the vertex form of 5y = -2x^2-7x+2?

Sep 29, 2017

Vertex form of equation is $y = - 0.4 {\left(x + 1.75\right)}^{2} + 1.625$

#### Explanation:

$5 y = - 2 {x}^{2} - 7 x + 2 \mathmr{and} y = - \frac{2}{5} {x}^{2} - \frac{7}{5} x + \frac{2}{5}$ or

$y = - 0.4 {x}^{2} - 1.4 x + 0.4 \mathmr{and} y = - 0.4 \left({x}^{2} + 3.5 x\right) + 0.4$ or

$y = - 0.4 \left({x}^{2} + 3.5 x + {1.75}^{2}\right) + 0.4 - \left({1.75}^{2} \cdot - 0.4\right)$ or

$y = - 0.4 {\left(x + 1.75\right)}^{2} + 0.4 + 1.225$ or

$y = - 0.4 {\left(x + 1.75\right)}^{2} + 1.625$ , comparing with standard vertex

form of equation y = a(x-h)^2+k ; (h,k) being vertex we find

$a = - 0.4 , h = - 1.75 , k = 1.625 \therefore$.

Vertex is at $\left(- 1.75 , 1.625\right)$ and vertex form of equation is

$y = - 0.4 {\left(x + 1.75\right)}^{2} + 1.625$ [Ans]