Graph quadratic functions in all forms

The  exercise appears under the Algebra I Math Mission and Algebra II Math Mission. This exercise practices graphing quadratic functions given in any form.

Types of Problems
There are two types of problems in this exercise:


 * 1) Graph the parabola given in standard form: This problem provides an equation of a parabola and a graphing plane. The student is asked to correctly graph the parabola on the plane using by dragging the three points. Graph quadratic functions in all forms.PNG
 * 2) Graph the parabola given in vertex form: This problem provides an equation of a parabola and a graphing plane in vertex form. The student is asked to correctly graph the parabola on the plane by dragging the three points. Graph quadratic functions in all forms2.PNG

Strategies
Knowledge of graphing quadratic equations in all forms will ensure success on this exercise, from a T-table to other more efficient methods.
 * 1) In the standard form a T-table can be the most efficient method to graph.
 * 2) If the vertex can be located, then symmetry ensures that values on one side will occur on the other side.
 * 3) If the given standard form of the parabola can be factored quickly, this will locate x-intercepts. Then the vertex is located half-way between the x-intercepts due to symmetry.
 * 4) In vertex form, follow this three-step process:
 * 5) Graph the vertex,
 * 6) Plot a second point treating the coefficient as if it were a "slope", and
 * 7) Plot the third point via symmetry over the axis of symmetry through the vertex.

Real-life Applications

 * 1) Quadratics are used to model many situations in physics and business.