SAT Math: Height h(t) = -16t² + 64t + 80, Find Time to Reach Maximum Height

Exact Question Text

<blockquote>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?</blockquote> <hr>

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.

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2. Fast Desmos / Calculator Shortcut

Graph y = -16x^2 + 64x + 80. Vertex apex point is at (2, 144). Answer: 2 seconds.

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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.