Question

In the context of the problem, the intersection point(s) of the graphs of the quadratic equations y=−6.1x^2+100x−180 and y=−412+80x−150 represent:

A) The maximum profit for selling soccer balls and footballs.

B) The break-even point for soccer balls and footballs.

C) The points where the daily profit is equal for selling soccer balls and footballs.

D) The minimum profit for selling soccer balls and footballs.

Answer 1

The intersection points of the given quadratic equations represent the points where the daily profit is equal for selling soccer balls and footballs.

Step-by-step explanation:

The quadratic equations are y=−6.1x^2+100x−180 and y=−412+80x−150. To find the intersection point, we can set the two equations equal to each other and solve for x. This gives us:

−6.1x^2+100x−180 = −412+80x−150

Combine like terms and simplify:

−6.1x^2+20x−2 = 0

Now, we can solve this quadratic equation by factoring or using the quadratic formula. After solving for x, we can substitute it back into one of the original equations to find the y-coordinate of the intersection point. These intersection points represent the points where the daily profit is equal for selling soccer balls and footballs, so the correct answer is C) The points where the daily profit is equal for selling soccer balls and footballs.