## Deriving the Formula of the Vertex of Quadratic Functions

In getting the vertex of the quadratic function in general form $f(x) = ax^2 + bx + c$, we usually need to convert it to the vertex form $f(x) = a(x - h)^2 + k$. In the latter form, the vertex of the parabola is at $(h,k)$. For example, the function in the general form

$f(x) = 2x^2 - 12x + 22$

can be rewritten in the vertex form as

$f(x) = 2(x - 3)^2 + 4$.

In the vertex form, it is easy to see that the vertex is at $(h,k) = (3,4)$.

Aside from this method, we can also use the ordered pair

$\left ( \dfrac{-b}{2a}, \dfrac{4ac - b^2}{4a} \right )$

in place of $(h,k)$» Read more