GPS Alignment: Instructor Page
Week 7: Algebra  Functions
Intersecting Functions (Printable PDF)
Given a quadratic function, y = Ax^{2} + Bx + C, how many times can a linear function, y = Ax +B intersect the parabola? Consider all cases.
GPS 
As seen in Problem Exploration 
M7A3: Students will understand relationships between two variables.
a. Plot points on a coordinate plane
b. Represent, describe and analyze relations from tables, graphs, and formulas.

This investigation involves analyzing the graphs of a linear and a nonlinear function. It will probably be helpful for the students to first graph them. 
M8A3: Students will understand relations and linear functions.
a. Recognize a relation as a correspondence between varying quantities.
b. Recognize a function as a correspondence between inputs and outputs where the output for each input must be unique.
c. Distinguish between relations that are functions and those that are not functions.
i. Identify relations and functions as linear or nonlinear.
j. Translate among verbal, tabular, graphic, and algebraic representations of functions.

The teacher can lead a discussion to cover the first three elements of this standard.
i. The student must be able to compare the graphs of linear and nonlinear functions. A discussion can be led by the teacher about the difference between linear functions and this parabola.
j. The student must also be able to translate between the equations of the functions and their graphs. 
M8A4: Students will graph and analyze graphs of linear equations.
c. Graph equations of the form y = mx + b.

In order to evaluate all possible cases, the student must be able to graph linear equations in the form y=mx+b. Further, they must understand what affect changing the values of m and b have on the graph. 
