# Question #53a4c

May 17, 2015

The vertex of the parabola $y = - 4 {x}^{2} + 8 x - 7$ is (1, -3).

Right away it's important to realize that this is a quadratic equation of the form $y = a {x}^{2} + b x + c$, so it will form a parabola.

The line of symmetry (or axis that passes through the vertex) of the parabola will always be -b/2a. "B" in this case is 8, and "a" is -4, so $- \frac{b}{2 a}$ = $- \frac{8}{2 \left(- 4\right)}$=$\frac{- 8}{-} 8$=$1$

This means the x value of the vertex will be 1. Now, all you have to do to find the y-coordinate is plug '1' in for x and solve for y:

$y = - 4 {\left(1\right)}^{2} + 8 \left(1\right) - 7$
$y = - 4 + 8 - 7$
$y = - 3$

So the vertex is (1, -3), as seen in the graph below (roll over the vertex to see the coordinates). graph{-4x^2 + 8x - 7 [-8.46, 11.54, -9.27, 1.15]}