Chapter 4 Quadratic Functions and Factoring - Mixed Review of Problem Solving - Lessons 4.6-4.10 - Page 316: 2c

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We have: $-0.8x^2+146x \gt 6500\\\Leftrightarrow-0.8x^2+146x-6500\gt 0 \\ \Leftrightarrow 4x^2-730x+32500 \lt 0 \\ \Leftrightarrow 2x^2-365x+16250\lt 0 \\ \Leftrightarrow x=\frac{365 \pm \sqrt 3225}{4}\approx 77105$ Graphing the concave down parabola of the original inequality $y=-0.8x^2+146x-6500$, the revenue will be above $\$6500$ when the price is in the interval $(77,105)$.