Question

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 1

Replace y in the equation with 50: (50 = -10x2 +160x - 430) Use factoring to solve the equation. After writing the equation in standard form and dividing each side by -10, it is easy to factor as 0 = (x - 4)(x - 12).

Explanation:

Answer 2

x = 4 or x = 12

Explanation:

Given:

y = -10x² + 160x - 430

When y = $50

50 = -10x² + 160x - 430

50 + 430 = -10x² + 160x

480 = -10x² + 160x

-10x² + 160x - 480 = 0

Divide through by -10

x² - 16x + 48 = 0

Solve the quadratic equation using factorization method

+48 = -12 × -4

-16 = -12 -4

Therefore,

-12 and -4 are both factors

x² - 16x + 48 = 0

(x - 4 )(x - 12 ) = 0

x - 4 = 0

x = 4

OR

x - 12 = 0

x = 12