Title
COEFFICIENTS THAT AFFECT THE GRAPH
Problem Statement
Explain how the graph of
the function h(x) = ax^{2} + 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) = ax^{2} + 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 = x^{2}. 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 = x^{2} + 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 = x^{2} + 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
