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Home » g(x) = \dfrac53x^3 - 6x^2 + \dfrac433x - 15. - Veritas Home Health

g(x) = \dfrac53x^3 - 6x^2 + \dfrac433x - 15. - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \( a_4 = 3a_3 + 4 = 3 \times 34 + 4 = 106 \)

📌 Problem:** A company’s profit \( P \) (in thousands) is modeled by \( P = -2x^2 + 12x - 5 \), where \( x \) is the number of units sold (in hundreds). What is the maximum profit?

📌 The profit function is a quadratic \( P = -2x^2 + 12x - 5 \), which opens downward.

📌 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?

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