Graphing parabolas in all forms

The  exercise appears under the Algebra I Math Mission. This exercise practices graphing parabolas.

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 graph the parabola on the plane using the graphing manipulative.Gpiaf2.png
 * 2) Graph the parabola given in vertex form: This problem provides an equation of a parabola and a graphing plane. The student is asked to graph the parabola on the plane using the graphing manipulative.Gpiaf1.png

Strategies
Knowledge of any graphing technique 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: 1) Graph the vertex, 2) plot a second point treating the coefficient as if it were a "slope", and 3) plot the third point via symmetry over the axis of symmetry through the vertex.

Real-life Applications

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