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).

Answer 2

EQUATION:
`x^2-16x+48=0`

METHOD: Factorization.

The sellings prices are:

$4

$12

Explanation:

You need to find the selling price or prices that would generate $50 in daily profit, then you need to substityte
`y=50` into the quadratic function:

`50=-10x^2+160x-430`

Make the equation equal to zero:

`-10x^2+160x-430-50=0\\-10x^2+160x-480=0`

Simplify by dividing by -10, then you obtain the equation:

`x^2-16x+48=0`

You can solve it with Factorization.

Choose two numbers whose sum is -16 and whose product is 48.

These would by -12 and -4.

Then:

`(x-12)(x-4)=0\\x_1=12\\x_2=4`