ResourceMAP - Quadratic Functions - Teacher Edition

ResourceMAP modules are relatively short and designed for flexible implementation; that is, they can be used in regular classes as well as in special test-preparation settings. Each module contains a set of contextual problems in several formats: multi-part open response, short response, and multiple-choice. Accompanying the problem set are tip sheets that serve several purposes including lists of formulas, calculator instruction, and brief reviews of the module's underlying mathematics. Also provided are teacher notes (the module purpose, the mathematical focus, and implementation commentary), answers to all problems, and (in a few cases) handout masters.

Quadratic Functions

From the effect of gravity to the stopping distance of a car, quadratic functions are
a useful tool for solving real-world problems. A quadratic function has the general
form

y = ax² + bx + c

where a, b, and c are constants. The graph of a quadratic function is a parabola.
Applications of quadratic functions often require the solution of a quadratic
equation.

I. Purpose
• To identify real-world situations in which quadratic functions are appropriate
models
• To use properties of quadratic functions to solve real-world problems

II. Mathematical Focus
• Quadratic functions
• Quadratic equations

III. Tip Sheets
Two Tip Sheets accompany this module.

• Fitting a Quadratic Function: This Tip Sheet discusses identifying a
situation as one in which a quadratic model is appropriate and using calculator
regression to fit a quadratic function.

• Solving a Quadratic Equation: This Tip Sheet discusses solving a
quadratic equation by factoring, by the Quadratic Formula, and by locating
x-intercepts on a graphing calculator. Also discussed is the use of a graphing
calculator to find the coordinates of a parabola’s vertex.