# How do I use the vertex formula to determine the vertex of the graph for y = -4x^2 + 8x?

May 1, 2015

The vertex of graph of $y = a {x}^{2} + b x + c$

has $x$-coordinate $x = - \frac{b}{2 a}$

So, the $x$-coordinate of the vertex of the graph of $y = - 4 {x}^{2} + 8 x$ is:

x= -(8)/(2(-4), which we can evaluate (simplify, calculate)

$x = - \frac{8}{2 \left(- 4\right)} = - \frac{8}{-} 8 = 1$,

To find the $y$-coordinate of the vertex, find the value of $y$, when $x = 1$

$y = - 4 {\left(1\right)}^{2} + 8 \left(1\right) = - 4 + 8 = 4$

The vertex is: $\left(1 , 4\right)$.