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

Describe how changing the coefficients (a, b, and c) in the function h(x) = ax2 + bx + c affects the graph of the function.

Plans to Solve/Investigate the Problem

Using a graphing calculator I plan to examine the effects of changing the coefficients to see how the graphs change in appearance.

1.      I plan to find out how changing a affects the function.

2.      I plan to find out how changing b affects the function.

3.      I plan to find out how changing c affects the function.

Investigation/Exploration of the Problem

1.      Begin by graphing y = x2.  Using a graphing calculator continue to graph variations of the function by changing the coefficient a in the problem.  From observation you will see that as the absolute value of a increases, the thinner the parabola formed by the quadratic function will become.  As the absolute value of a decrease the wider the parabola formed by the quadratic function will become.  If the coefficient of a is positive the parabola will open upward and if the value of a is negative the parabola will open downward.

2.      Begin by graphing y = x2 + 1x.  Using a graphing calculator continue to graph variations of the function by changing the coefficient b in the problem.  From observation you will see that changing the value of the coefficient b will shift the parabola diagonally.  Positive values of b will shift the parabola left and down and negative values of b will shift the parabola down and right.

3.      Begin by graphing y = x2 + 1x + 1.  From observation you will see that as the value of c changes, the parabola move up that number of units if c is positive and down that number of units if c is negative.

Author & Contact
Insert name and contact information.
mailto:lparsons@rockdale.k12.ga.us