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