# How do you write a quadratic function in vertex form whose graph has the vertex (-3,5) and passes through the point (0,-14)?

Apr 24, 2018

$y = - \frac{19}{9} {\left(x + 3\right)}^{2} + 5$

#### Explanation:

If an equation representing a parabola is in vertex form such as

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

then its vertex will be at $\left(k , h\right)$. Therefore the equation for a parabola with a vertex at (-3, 5), will have the general form

$y = a {\left(x + 3\right)}^{2} + 5$

If this parabola also passes through the point $\left(0 , - 14\right)$ then we can determine the $a$ parameter.

$- 14 = a {\left(0 + 3\right)}^{2} + 5$

$9 a = - 19$

$a = - \frac{19}{9}$

So our equation in vertex form is

$y = - \frac{19}{9} {\left(x + 3\right)}^{2} + 5$

graph{-19/9(x+3)^2+5 [-10, 2, -20, 10]}