Lesson Title : Parabolic Equation of a Catapult
Course Title : Algebra 2 / Precalculus
Instructor : Ellen Byron
Materials : Small Catapult with projectile object. Contact Sierra College STEM project for
assembly of a catapult.
Resources : Algebra 2 textbook or Precaclulus textbook to assist student with exploration of
parabolic equations.
Time for Lesson : One or Two class periods (one if on block schedule) plus homework time. An
additional 3 hour time slot allocated to building the STEM catapult.
Objective : Linking the study of parabolic equations to real-life applications. Students will
collect data and write a parabolic equation of a catapult (trajectory) using the quadratic equation.
Course Standards:
8.0 Students solve and graph quadratic equations by factoring, completing the square, or
using the quadratic formula. Students apply these techniques in solving word problems.
They also solve quadratic equations in the complex number system.
9.0 Students demonstrate and explain the effect that changing a coefficient has on the graph
of quadratic functions; that is, students can determine how the graph of a parabola changes
2
as a, b, and c vary in the equation y = a(x-b) + c.
10.0 Students graph quadratic functions and determine the maxima, minima, and zeros of
the function.
Anticipatory Set:
1. Students must have enough catapults to form groups of 4-5 each. You can purchase
catapult kits or contact Sierra College STEM project to arrange a separate lesson to
manufacture the catapults as a class.
2. Have each group open their textbooks and write the standard form of the parabola
equation. Let the students have a discussion of the different elements of the standard
equation and how the group could possibly collect data using the catapult to write
an equation. Make sure they talk about the vertex and sign of a (must be negative as
the parabola is facing down).
This unit developed under funding provided by California Community College Chancellor’s Office grant 08-315-003.
Lesson using y=a (x-h)2 +k .
Materials (need enough for each group in class):
1. Catapults with ball
2. Long tape measure
3. Yard stick
4. Data Collection Handout (enclosed)
5. Video camera (optional). Students could use their phones to video the trajectory if
allowed.
Lesson
1. Students will need to determine the vertex of the parabola as well as an additional point
on the parabola (the endpoint) to determine the equation of the trajectory.
2. Ask students how they could determine the exact point of the vertex? This point is
located exactly halfway (half the range) between the starting point and ending point.
Have students lie out the tape measure and one student shoots the ball a few times while
another group member records the exact location of the ending point. Make sure students
use the launching attachment on the catapult provided so that the launch angle is the
exactly the same each time. That will ensure the same trajectory every time.
3. Close the classroom door to ensure the ball does not fly out the door.
4. Note: Depending on the catapult you use, you might be launching the ball above the
ground level, which alters the range. Most catapults launch from close enough to the
ground that students will create a mostly accurate equation. To get a more accurate
equation, please look for the lesson plan for Precalculus that utilizes the height of the
launch.
5. Log the ending points on the worksheet and take the average. You can now determine the
x value of your vertex by dividing the ending point in half.
6. To determine your y value of the vertex, first find the location (x coordinate) of where
you will measure the height of the trajectory. After they have located the place to record
the measurement, have students shoot the ball once more as a trial run to get an idea of
how high the yard stick must be attached to the wall (or be held by a student) to make a
reading. Once set, have the group launch the trajectory and either record the launch on a
video camera or have one student stand back and read the height on the yardstick. Make
sure to make at least three readings for accuracy.
7. Now each group has the exact location of the vertex (both h and k values) and can place
these values into their equation.
8. To determine the value of “a “(should the final value of a be negative or positive for this
problem?), use two known points that lies on your trajectory ( both your starting and
ending points) and determine the value of a for both. How do the values of a compare?
Should they be exactly the same? Which value is more accurate? (the starting point is
slightly above the ground so it’s x value is an estimate)
This unit developed under funding provided by California Community College Chancellor’s Office grant 08-315-003.
Supplemental Lesson for the Sierra College STEM catapults.
1. Once students calculate the equation of their catapult, set up a bucket either inside or
outside your classroom.
2. Task: Each group will get 15 minutes to determine the placement of their catapult in the
vicinity of the bucket. Encourage they use the information collected in the previous
exercise to help them locate the placement.
3. Let each group mark their location with tape prior to beginning the contest(if one group
hits the bucket, subsequent groups would just copy the place of the successful group).
Allow them only one or two trial shots when placing their tape to make sure they THINK
about the placement of the catapult.
4. Each group gets 4 shots. Record the number of times each group hits the bucket.
5. As the teacher, you can decide the reward for the winning team.
This unit developed under funding provided by California Community College Chancellor’s Office grant 08-315-003.
Date: _______________
Group Names: ___________________
___________________
___________________
Data Collection for Parabola Standard Equation y=a (x-h)2 +k
Range
Reading 1
Reading 2
Reading 3
Reading 4
h value average
Reading 1
Reading 2
Reading 3
Reading 4
k value average
Height
Record Vertex
(
,
)
Equation Calculation
x
y
Equation Substitution
Coordinate Coordinate y=a (x-h)2 +k
Solve for a
Origin
Ending Point
Final Equation for Catapult Trajectory: _________________________
This unit developed under funding provided by California Community College Chancellor’s Office grant 08-315-003.
Catapult Target Competition
Group Name
Successful Target Shots
This unit developed under funding provided by California Community College Chancellor’s Office grant 08-315-003.