Question

Y = - 6 x² + 100 x - 180 x. The vertex is located at (8.33, 236.67). What does this point represent in context? Choose two correct answers.

1) The maximum profit from selling soccer balls
2) The number of soccer balls sold at maximum profit
3) The minimum profit from selling soccer balls
4) The number of soccer balls sold at minimum profit
5) The cost price of each soccer ball

Answer 1

The vertex (8.33, 236.67) of the quadratic equation represents the number of soccer balls sold at maximum profit (8.33) and the maximum profit from selling soccer balls (236.67).

Step-by-step explanation:

The equation Y = -6x² + 100x - 180x represents a quadratic equation, and its vertex represents a significant point on the graph. Since the equation can be related to a real-world context such as profit, the vertex (8.33, 236.67) corresponds to two distinct interpretations:

• The first value in the vertex, x-coordinate 8.33, represents the number of soccer balls sold to achieve the maximum profit.
• The second value in the vertex, y-coordinate 236.67, represents the maximum profit from selling soccer balls.

The negative coefficient of the x² term indicates that the parabola opens downward, meaning that the vertex corresponds to the maximum point on the curve.