solve P=-¼x²+5x+24 when Your company has a profit that is represented by the equation P= -¼x²+5x+24, where P is the profit in millions and x is the number of years starting in 2018.

Answer 1

To solve for the profit equation P = -¼x² + 5x + 24, we can set P to zero and find the values of x that make the equation true. This will give us the years when the profit would be zero or break-even.

0 = -¼x² + 5x + 24

Multiply the equation by -4 to eliminate the fractions:

0 = x² - 20x - 96

Now, we can try to factor the equation:
0 = (x - 12)(x + 8)

Setting each factor to zero and solving for x:
x - 12 = 0 or x + 8 = 0

x = 12 or x = -8

Since x represents the number of years starting from 2018, we can see that x = 12 corresponds to the year 2030, and x = -8 does not make sense in this context.

Therefore, in the profit equation P = -¼x² + 5x + 24, the profit will be zero or break-even in the year 2030.