The quadratic equation y = –6x2 + 100x – 180 models the store’s daily profit, y, for selling soccer balls at x dollars.The quadratic equation y = –4x2 + 80x – 150 models the store’s daily profit, y, for selling footballs at x dollars. Use a graphing calculator to find the intersection point(s) of the graphs, and explain what they mean in the context of the problem.

Answer:The point of intersections are (1.838, -16.49) and (8.16, 236.49). The point (1.838, -16.49) represent that the loss for selling soccer balls equals loss for selling footballs when they are sold at a price of 1.84 dollars and the loss is $16.49.The point (8.16, 236.49) represent that the profit for selling soccer balls equals profit for selling footballs when they are sold at a price of 8.16 dollars and the profit is $236.49.Step-by-step explanation:Given:The daily profit expression for selling soccer balls is given as:[tex]y=-6x^2+100x-180[/tex]The daily profit expression for selling footballs is given as:[tex]y=-4x^2+80x-150[/tex]The graph is drawn as shown below. From the graph, the points of intersection of the two functions are (1.838, -16.49) and (8.16, 236.49).Therefore, for selling price equal to 1.84 dollars, there is negative profit which means they will have loss. The daily loss for selling both soccer balls and footballs would be same and equal to $16.49.For selling price equal to 8.16 dollars, there is positive profit. The daily profit for selling both soccer balls and footballs would be same and equal to $236.49.