Students investigate how quadratic equations model rocket flight and how shifts, stretches, compressions, and reflections change predicted and actual trajectories. After analyzing movie launches and consulting Jim, a rocket scientist, teams design and test rockets while identifying each path’s vertex, intercepts, axis of symmetry, domain, and range. Students use test data, debrief circles, peer critique, and successive revisions to strengthen their mathematical models, teamwork, and communication. They demonstrate learning through a launch portfolio and trajectory portfolio board presented at the Trajectory Tech Showcase.

Students will model rocket flight with quadratic functions and interpret the vertex, intercepts, axis of symmetry, domain, and range in relation to an actual launch path. They will predict and explain how shifts, stretches, compressions, and reflections change an equation, its graph, and the rocket’s trajectory. Through iterative launch tests, peer critique, debrief circles, and feedback from Jim the rocket scientist, teams will analyze discrepancies, revise their models, and make shared design decisions. Students will communicate their reasoning and growth through a launch portfolio, trajectory board, and presentation at the Trajectory Tech Showcase.

Teams will create rocket design sheets, quadratic equations, graphs, flight predictions, and test-data records identifying the vertex, intercepts, axis of symmetry, domain, and range. After each test, they will add predicted and actual paths to a shared chart, record peer and Jim’s feedback, revise an equation or launch angle, and complete a launch-debrief reflection on transformations and teamwork. Each student will compile these artifacts into a launch portfolio with notes explaining how shifts, stretches, compressions, or reflections changed the trajectory and how the contextual domain matched the flight. The final trajectory portfolio board will present successive revisions, recorded results, and conclusions at the Trajectory Tech Showcase.

Students watch short clips of famous movie rocket launches, marking the launch point, highest point, and landing point they observe. Teams sketch a predicted parabolic path, label its vertex, intercepts, axis of symmetry, domain, and range, and discuss which real-world factors could change the trajectory. Jim the rocket scientist then shares a brief launch scenario and challenges teams to revise one coefficient to predict a shift, stretch, compression, or reflection. The class closes by generating initial responses to the two essential questions and posting predictions for later testing and revision.

Host a Trajectory Tech Showcase where teams present portfolio boards featuring rocket designs, revised equations, graph transformations, predictions, and recorded test data. Invite Jim the rocket scientist, families, and other students to ask teams how the domain matched the actual flight path and how equation changes affected the trajectory. Conclude with a gallery walk and brief team reflections highlighting one successful revision, one collaboration strength, and one next-step question.