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.

Problem setup

Using a graphing calculator examine the effects of changing the coefficient to see how the graph changes.

Plans to Solve/Investigate the Problem

Input different values for a, b, c.  Graph quadratic equation using calculator.  Try to keep the x fixed and evaluate the change in y.

Investigation/Exploration of the Problem

*For a as the coefficient gets bigger the y value gets bigger. (parabola opens)

As the absolute value of a increases, the value of y increases. (parabola narrows)

As the absolute value of a decreases, the value of y decreases. (parabola widens)

If the coefficient of a is positive, the parabola will open upward.

If the coefficient of a is negative, the parabola will open downward.

*For b, if the coefficient is negative, the parabola will translate (slide) right.  If the coefficient is positive, the parabola will translate left.

*For c, a change will create a translation.

Author & Contact
llaster@frockdale.k12.ga.us

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