Intermath | Workshop Support

 Write-up

Title
Coefficients that affect the graph

Problem Statement
Explain how the graph of the function h(x) = ax2 + bx + c changes when you modify a, b, and c.

Plans to Solve/Investigate the Problem

I plan to use a graphing calculator to investigate the problem.

Investigation/Exploration of the Problem

Choosing values for a:

As the value of “a” increases (choosing positive values for a) the graph of the parabola narrows more quickly because the y values increase at a faster rate. Choosing negative values for “a” will reflect the parabola over the x axis.

Choosing values for b:

As the value of “b” increases the graph of the parabola shifts to the left.  If the value of “b” is negative the graph will shift right. The line of symmetry is no longer the y axis. The vertex also shifts downward.

Choosing values for c:

As the value of “c” changes, the vertex of the parabola shifts up or down.  If “c” is a positive value the graph shifts upward and if “c” is a negative value the graph shifts downward. “C” is the y-intercept. It is where the graph crosses the y axis.

Dottie Mitcham

Link(s) to resources, references, lesson plans, and/or other materials