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Home » \Delta = b^2 - 4ac - AIKO, infinite ways to autonomy.

\Delta = b^2 - 4ac - AIKO, infinite ways to autonomy.

📅 May 3, 2026 👤 scraface

May 03, 2026

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A company's profit is modeled by \(P(x) = -2x^2 + 80x - 150\), where \...
The vertex form is used for maximum: \(x = -\frac{b}{2a}\).
Here, \(a = -2\), \(b = 80\).
\(x = -\frac{80}{2 \times -2} = 20\).
Maximum profit: \(P(20) = -2(20)^2 + 80(20) - 150\).
\(= -800 + 1600 - 150 = 650\).
The sum of the first \(n\) positive integers is 5050. Find \(n\).
Formula: \(\frac{n(n+1)}{2} = 5050\).
\(n(n+1) = 10100\).
\(n^2 + n - 10100 = 0\).

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