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4545 center blvd - Decision Point

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 The vertex occurs at \( x = -\frac{b}{2a} = -\frac{12}{2(-2)} = 3 \).

📌 Substitute \( x = 3 \):

📌 \( P = -2(3)^2 + 12(3) - 5 = -18 + 36 - 5 = 13 \).

📌 The maximum profit is 13 thousand dollars, or $13,000.

📌 Problem:** A ball is thrown upward from a height of 2 meters with a velocity of 20 m/s. Its height \( h(t) = -5t^2 + 20t + 2 \). When does it hit the ground?

📌 \( -5t^2 + 20t + 2 = 0 \)

📌 Use quadratic formula: \( t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)

📌 \( a = -5, b = 20, c = 2 \)

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