Note

Revise.

To get the co-ordinates of the maximum/minimum turning point.

$(x + h) = 0$ or $-h$ provides the $x$ co-ordinate. $k$ provides the $y$ co-ordinate.

Methodology

Formula

Warning

Not recommended - harder remember.

Note: follows variable naming in quadratics: $ax^2 + bx + c$.

This can be used to calculate the midpoint of a Quadratic as well.

Forming Equations

You can also do the inverse to work out an quadratic equation from constants produced.

$h$ is provided by the inverse of the $x$ co-ordinate, this is for the $y$ co-ordinate. $k$ is the local min/max y co-ordinate.

however this leaves you with:

which you can use a co-ordinate to calculate $a$:

Using $(40. 0)$ with $y = 12$ and $x = 20$.