\( -5t^2 + 20t + 2 = 0 \)
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- \( P = -2(3)^2 + 12(3) - 5 = -18 + 36 - 5 = 13 \).
- 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?
- Use quadratic formula: \( t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)
- \( a = -5, b = 20, c = 2 \)
- Discriminant: \( 20^2 - 4(-5)(2) = 400 + 40 = 440 \)
