# How do you write the equation of the parabola in vertex form given the vertex (-2, -8) and passes through the point (7, -494)?

Feb 17, 2016

$y = - 6 {\left(x + 2\right)}^{2} - 8$

#### Explanation:

The equation of a parabola in vertex form is

$y = a {\left(x - h\right)}^{2} + k$
where (h , k ) are the coords of the vertex.

here the coords of the vertex are given and so

$y = a {\left(x + 2\right)}^{2} - 8$

now also given a point (7 , -494) that the parabola passes thro'.
substitute x = 7 and y = -494 into the equation and solve for a.

hence -494 = 81a - 8 → a = -6