# How do you find the rule of a quadratic function whose graph has given vertex of (4,5) and passes through the given point of (6,17)?

Oct 31, 2016

You have not given enough information to rule out one of two possible configurations. Please see the explanation.

#### Explanation:

There are two possible configurations:

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

and

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

where $\left(h , k\right)$ is the vertex.

Substituting the vertex, $\left(4 , 5\right)$, and the point $\left(6 , 17\right)$ into both and then solving for the respective values of a:

$17 = a {\left(6 - 4\right)}^{2} + 5$

and

$6 = a {\left(17 - 5\right)}^{2} + 4$

Solve for a:

$a = 3$

and

$a = \frac{1}{72}$

The two possible equations are:

$y = 3 {\left(x - 4\right)}^{2} + 5$

and

$x = \frac{1}{72} {\left(y - 5\right)}^{2} + 4$