# What is the the vertex of y=2x^2 + 8x + 5?

Jan 8, 2016

(-2,-3)

#### Explanation:

Well there are numerous ways to solve this but I'll tell you the shortest one (at least according to me).

When you see a parabola of form $y = a {x}^{2} + b x + c$ the slope of its vertex is 0. We know that the formula of the slope of any instantaneous line is $\frac{\mathrm{dy}}{\mathrm{dx}}$ so

$d \frac{2 {x}^{2} + 8 x + 5}{\mathrm{dx}} = 0$
On solving this we get $x = - 2$

Put this in our original equation of parabola and $y = - 3$

This coordinates of the vertex are (-2,-3)