Find features of quadratic functions

The  exercise appears under the Algebra I Math Mission. This exercise draws attention to several key features of a quadratic function.

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


 * 1) Find the zeros, vertex and symmetry of the quadratic: This problem provides a quadratic function. The student is asked to identify three core components of the parabola: the zero(s), the vertex, and the axis of symmetry.Kfoqf1.png

Strategies
Knowledge of the quadratic formula can help lead to all elements of this, although vertex form can also be used for some parts.
 * 1) The zeroes can be found by the quadratic formula, which is $$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$.
 * 2) The vertex is located at $$(\frac{-b}{2a},f(\frac{-b}{2a})$$.
 * 3) The axis of symmetry on this problem is always vertical, located at $$x=\frac{-b}{2a}$$.

Real-life Applications

 * 1) The zeroes of a quadratic are used to find many physical interpretations, such as equilibrium prices in supply-demand applications and objects hitting the ground in physics.
 * 2) The vertex is a relative extremum in general, and absolute extremum in the case of a quadratic.
 * 3) The axis of symmetry can assist with many graphing applications in art and architecture.