# How do you write the equation of the parabola in vertex form given vertex (-4,-7) and also passes the point (-3,-4)?

Jan 31, 2017

There are 2 equations, one of the form, $y = a {\left(x - h\right)}^{2} + k$, and the other of the form, $x = a {\left(y - k\right)}^{2} + h$. Where $\left(h , k\right)$ is the vertex and you solve for "a" using the given point.

#### Explanation:

Given the vertex $\left(- 4 , - 7\right)$ and passes through the point $\left(- 3 , - 4\right)$

Using the first form:

$y = a {\left(x - - 4\right)}^{2} - 7$

Substitute -3 for x and -4 for y:

$- 4 = a {\left(- 3 - - 4\right)}^{2} - 7$

$3 = a {\left(1\right)}^{2}$

$a = 3$

The first equation is:

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

Here is the graph of the equation and the two points:

Using the second form:

$x = a {\left(y - - 7\right)}^{2} - 4$

Substitute -3 for x and -4 for y:

$- 3 = a {\left(- 4 - - 7\right)}^{2} - 4$

$1 = a {\left(3\right)}^{2}$

$a = \frac{1}{9}$

The second equation is:

$x = \frac{1}{9} {\left(y - - 7\right)}^{2} - 4$

Here is the graph of the equation and the two points: