Question

The graph of the function P(x) = −0.34x2 + 12x + 62 is shown. The function models the profits, P, in thousands of dollars for a tire company, where x is the number of tires produced, in thousands:

Answer 1

Answer: 1.12 ≤ x ≤ 34.18

Step-by-step explanation

As the company wants to keep its profits at or above $75,000, we have to search for those values of tires produce (x) that maintain the profits at or above $75,000. Based on this we can conclude that the negative numbers do not give this profit, and 0 tires is below $75,000. Thus, the best approximation is:

Additionally, we can prove this by making the function equal 75:

`75=−0.34x^2+12x+62`
`0=−0.34x^2+12x+62-75`
`0=−0.34x^2+12x-13`

Using the General Quadratic Formula we get that:

`x_1=1.12`
`x_2=34.18`