# How do you write the equation of the parabola in vertex form given vertex is at (-1, 17) and the parabola passes through the point (0, 6)?

Feb 21, 2016

$y = - 11 {\left(x + 1\right)}^{2} + 17$

#### Explanation:

The equation of a parabola in vertex form is

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

here the vertex = (-1 , 17 ) and so equation is

$y = a {\left(x + 1\right)}^{2} + 17$

Since the point (0 , 6) lies on the parabola it will satisfy the equation and by substituting the coordinate point , will allow a to be found.

hence  6 = a(0+1)^2 + 17 → 6 = a +17 → a = - 11

$\Rightarrow y = - 11 {\left(x + 1\right)}^{2} + 17$