Amusement Park Engineering // Vertex & Axis of Symmetry
TRACK ENGINEER BRIEFING:
Objective: Design 12 coaster hills and drops by physically marking the vertex \( (h, k) \) of each quadratic track equation \( y = ax^2 + bx + c \) — right on the blueprint.
How to Build: Compute \( h = \tfrac{-b}{2a} \), then drag the 🟡 vertex marker onto the curve's peak or valley, and drag the axis handle to line up with it. No multiple choice — your hands are the engineering tool.
Cart Integrity: You start with 3 test carts. A wrong placement sends a cart into a wobbly, comedic derailment. Losing all 3 shuts down the track.
Track Randomization: Track equations are shuffled every design session.
Test Run Animation: Nail the vertex + axis and a real test-cart rolls down your actual parabola with gravity-style speed — fast in the dips, slow over the peaks!
Session Memory: This blueprint console holds data only in active memory. Reloading the page resets the design log completely.
Please enter your name before opening the design deck!
Hill 01: Track Blueprint
DRAG THE VERTEX & AXIS ONTO THE TRACK TO CLEAR THE TEST RUN
Hill01 / 12
Cart Integrity🎢🎢🎢
Track Steepness
Score0 PTS
Track Equation (Standard Form)
Loading track blueprint...
Drag the vertex marker along the curve onto the peak or valley.
Drag the axis handle (dashed line) to match that x-position.
Vertex guess: —Axis guess: —
TRACK SHUTDOWN // CARTS DERAILED
All 3 test carts derailed from incorrect vertex calculations.
Final Design Score: 0 PTS
🧑🎓 Player: Student
Progress isn't saved — save this screen now to show your teacher your attempt.
GRAND OPENING APPROVED
Certified Coaster Vertex Engineer
Incredible engineering! You correctly located the vertex and axis of symmetry for every hill and drop, completing all test runs safely.
Total Design Score: 1200 PTS
🧑🎓 Player: Student
Progress isn't saved — save this screen now as proof of completion for your teacher.