Question

A company's profit (in millions of dollars) can be represented by x^2-6x+12, where x is the number of years since the company started. When did the company have a profit of $4 million?
I got two years, but I wanted to check this against something. Thanks in advance!

Answer 1

The function that models the profit of the company in million of dollars is:

$P= x^{2} -6x+12$

where x represents the number of years since the company started. We want to find when the profit of the company was $4 million. Setting P as 4 in above equation, we can find the value of x when the profit was $4 million.

$4= x^{2} -6x+12 \\ \\ x^{2} -6x+8=0 \\ \\ x^{2} -2x-4x+8=0 \\ \\ x(x-2)-4(x-2)=0 \\ \\ (x-2)(x-4)=0 \\ \\ x=2, x=4$

Thus, we can conclude that the profit of the company was $4 million in 2nd and 4th year