# What is the quadratic equation containing (5, 2) and vertex (1, –2)?

Nov 12, 2014

Vertex Form

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

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

By Vertex Form with $\left(h , k\right) = \left(1 , - 2\right)$, we have

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

By plugging in $\left(x , y\right) = \left(5 , 2\right)$,

$2 = a {\left(5 - 1\right)}^{2} - 2 = 16 a - 2$

by adding $2$,

$\implies 4 = 16 a$

by dividing by $16$,

$\implies \frac{1}{4} = a$

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