Digital SAT Math
SAT Math: Height h(t) = -16t² + 64t + 80, Find Time to Reach Maximum Height
• Direct Answer / Key Takeaway
Time to max height is at vertex t = -b / (2a) = -64 / (2 * -16) = -64 / -32 = 2 seconds.
Exact Question Text
A projectile is launched upward with height modeled by h(t) = -16t^2 + 64t + 80, where t is seconds. At what time t does the projectile reach its maximum height?
1. Step-by-Step Formal Solution
- Vertex t = -b / (2a) = -64 / (2 * -16) = 2.
- Maximum height is h(2) = -16(4) + 64(2) + 80 = -64 + 128 + 80 = 144 ft.
2. Fast Desmos / Calculator Shortcut
Graph y = -16x^2 + 64x + 80. Vertex apex point is at (2, 144). Answer: 2 seconds.
3. Distractor Trap Analysis
- Trap A (Sign Flip): Forgetting to reverse inequality or dropping negative sign.
- Trap B (Partial Evaluation): Solving for intermediate variable and stopping early.
- Trap C (Extreme Assumption): Over-inferring beyond textual evidence.
- Option Correct: Accurately satisfies all algebraic and logical constraints.
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