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Here, \( a = 1, b = -4, c = -10 \)
\( t = \frac{4 \pm \sqrt{16 + 40}}{2} \)
\( t = \frac{4 \pm \sqrt{56}}{2} \)
\( t = \frac{4 \pm 2\sqrt{14}}{2} \)
\( t = 2 \pm \sqrt{14} \)
Only the positive root is meaningful: \( t = 2 + \sqrt{14} \approx 5.74 \) seconds
#### 5.74 seconds
A company’s profit \( P(x) \) in thousands of dollars is modeled by the function \( P(x) = -2x^2 + 40x - 150 \), where \( x \) is the number of units sold in hundreds. What is the maximum profit and how many units must be sold to achieve it?
The vertex form of a parabola \( ax^2 + bx + c \) reaches maximum at \( x = -\frac{b}{2a} \)
Here, \( a = -2, b = 40 \)