Mathematics Discovery Lab – Quadratics 1
Problem/Question
How can predict how wide a quadratic graph is by looking at the coefficient ‘c’.
Background Information
A quadratic function has to have an x2 term
The standard form of a quadratic function is ax2 + bx + c
‘a’, ‘b’ and ‘c’ are coefficients of x
The graph of a quadratic function is a parabola (u-shaped graph)
Hypothesis
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Materials
Graphing Calculator
Pencil
Procedure
1.
2.
3.
4.
5.
Make a table of values for each function
Plot the coordinate points
Join the points with a smooth curve
Label the graph
Compare the width of each graph against the coefficient ‘a’
Results (5 points: accurate, neat, procedure followed)
y = x2
x
2
1
0
-1
-2
y=2x2
y = x2
y
x
2
1
0
-1
-2
y = -x2
x
2
1
0
-1
-2
y = 2x2
y=3x2
y
x
2
1
0
-1
-2
y=-2x2
y = -x2
y
x
2
1
0
-1
-2
y = -2x2
y = 3x2
y
y=-3x2
y
x
2
1
0
-1
-2
y = -3x2
y
‘
c
’
i
s
a
c
o
Conclusions (10 points: meaningful, detailed, accurate)
(Answer questions and interpret results in five or more complete sentences in paragraph form.)
What is a coefficient? What happens to the graph as the coefficient of x2 increases? What happens to
the graph as the coefficient decreases? What happens to the graph if the coefficient is negative? Why?
Predict what the graph of y=-5x2 looks like. Predict what the graph of y=⅛x2 looks like.
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