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.

Answer:

To find the selling prices that generate a $50 profit, replace y with 50 in the equation: 50 = –10x² + 160x – 430. Next, rewrite the equation in standard form by subtracting 50 from both sides to get 0 = –10x² + 160x – 480. Factoring is the best method because the entire equation can be divided by –10 to get 0 = x² – 16x + 48, which easily factors into (x – 4)(x – 12) = 0. This results in selling prices of $4 or $12.