# How do you write the quadratic in vertex form given vertex (2,3), point (3, -8)?

May 1, 2015

Given the vertex is at $\left(2 , 3\right)$
the vertex form of the equation is
$y = a \left(x - 2\right) + 3 \text{ for some constant value } a$

If the point $\left(3 , - 8\right)$ is a solution for this quadratic
$- 8 = a \left(3 - 2\right) + 3$
$- 8 = a + 3$
$a = - 11$

The vertex form of the quadratic with the given vertex and point is
$y = \left(- 11\right) \left(x - 2\right) + 3$