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📅 March 14, 2026 👤 scraface

Mar 14, 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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5Question: Let $ g(x^2 + 2) = x^4 + 4x^2 + 5 $. Find $ g(x^2 - 2) $.
g(x^2 + 2) = x^4 + 4x^2 + 5
We aim to find $ g(x^2 - 2) $.
Let’s define a substitution to help simplify. Let:
u = x^2 + 2 \Rightarrow x^2 = u - 2
x^4 = (x^2)^2 = (u - 2)^2 = u^2 - 4u + 4
Substituting into the expression for $ g(u) $:

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