Vertex of a parabola

The  exercise appears under the Algebra I Math Mission. This exercise practices calculating the vertex of a quadratic function.

Types of Problems
There is one type of problem in this exercise:


 * 1) Find the vertex of the parabola: This problem provides a quadratic function written in standard form. The student is asked to find the vertex of the parabola that is represented by the function.Voap1.png

Strategies
Knowledge of the process to find the vertex by algebra is sufficient for accuracy and efficiency, but completing the square provides better understanding for use in other contexts.
 * 1) The vertex is located at $$(\frac{-b}{2a},f(\frac{-b}{2a})$$.
 * 2) Completing the square assists with eventually graphing parabolas and can be used to prove the quadratic formula.

Real-life Applications

 * 1) The vertex is a relative extremum in general, and absolute extremum in the case of a quadratic.
 * 2) Since the vertex is an extremum, it can be used to find relative minimum and relative maximum values of several applications across business and science.