The quadratic function y = –10x2 + 160x – 430 models a store’s daily profit (y) for selling a T-shirt priced at x dollars. What equation do you need to solve to find the selling price or prices that would generate $50 in daily profit? What method would you use to solve the equation? Justify your choice.

Question

Revolt · Accepted Answer

Set 50 = -10x² + 160x - 430. Write the equation in standard form and divide by -10 to get x² - 16x + 48 = 0, which factors as (x - 4)(x - 12) = 0. Use factoring because the equation factors easily. The selling prices are $4 and $12.

Modeling with Quadratic Equations

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