
Nov. 3, 2000
Joanne
Pirog
Lesson Plan I Frameworks‑
Patterns, Relations and Algebra Analyze
and graph Quadratic functional relationships
Pass out graph paper to the
class. Ask them to investigate what the graph of y=lx^2 looks like by substituting lots
of points for x. Ask them what shape their graph looks like? Tell them that this u‑shaped
graph is called a parabola. Next, have the students graph y‑‑
‑1x ^2. Ask them how this graph looks
different than the first parabola they graphed? With several other examples
have the students try to determine what effect a positive coefficient of the x^2 term vs.
a negative coefficient of the x^2 term has on the graph of the parabola. A
positive coefficient makes
the curve look like Mwhile
a negative coefficient makes the curve look like L
An
important lesson from this activity for the Trebuchet Project will be for them to
realize that the graph of the path of a projectile launched by the Trebuchet will
be that of an upside‑down u‑shaped parabola. They will soon
realize that
the graph of the parabola y = ‑2x^2 + x will be this upside‑down u‑shape.
Next
explain to the class how these upside down parabola graphs have a maximum
vertex point. Demonstrate
with a diagram how the projectile will achieve a maximum height in the air
before coming down again. Graph
examples of parabolas such as y = ‑ I x^2+1 and y = ‑1 x^2 ‑2 and have the class find
all the maximum vertices of the graphs.
Finally explain to the students that the actual path
of a projectile launched by the Trebuchet is L
‑16T^2+ (v sin theta) T = 0. It is the ‑16 coefficient that produces the L
path. T = 5
sec, theta is the angle of release of the arm and H=O when the projectile lands again. The best angle of
release is supposedly an angle of 45 degrees because the penny launched
travels the farthest while the maximum height that it achieves
is kept at a minimum. 
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