# how do you change y=-2x^2+8x-1 to vertex form?

Mar 29, 2018

When given a quadratic equation $y = a {x}^{2} + b x + c$, the x coordinate of the vertex is, $h = - \frac{b}{2 a}$ and the y coordinate of the vertex is $k = a {\left(h\right)}^{2} + b \left(h\right) + c$ then use the form $y = a {\left(x - h\right)}^{2} + k$

#### Explanation:

Applying the information in the answer to the given equation:

$h = - \frac{8}{2 \left(- 2\right)}$

$h = 2$

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

$k = 7$

Substitute $a = - 2 , h = 2 , \mathmr{and} k = 7$ into the form:

$y = - 2 {\left(x - 2\right)}^{2} + 7$