Question

A florist sells different types of bouquets. after a research study, the florist concluded that the daily profit, in dollars, on sales X small bouquets is mixed by function f(x) = -3x² + 90x - 432. which statement about the function is true?

A) The function models the daily profit of the florist based on the number of small bouquets sold.
B) The coefficient of the x² term (-3) indicates a quadratic relationship in the profit function.
C) The maximum daily profit occurs when the number of small bouquets sold is at the vertex of the parabolic function.
D) The constant term (-432) represents the fixed costs incurred by the florist.
E) The function suggests that as the number of small bouquets sold increases, the daily profit decreases.

Answer 1

The true statement regarding the florist's profit function is that it models the daily profit based on the sale of small bouquets, where the profit has a quadratic relationship and reaches a maximum at the vertex of the parabola. Therefore the correct answer is Option A.

Step-by-step explanation:

The statement about the florist's daily profit function, f(x) = -3x² + 90x - 432, that is true is that the function models the daily profit of the florist based on the number of small bouquets sold. This function is a quadratic equation, indicated by the coefficient of the x² term, which in this case is -3, suggesting a parabolic shape of the graph. The maximum daily profit occurs at the vertex of the parabola. However, the constant term (-432) does not represent fixed costs, rather it is part of the calculation of total profit or loss. As in any quadratic function with a negative leading coefficient, the profit increases to a maximum point (vertex) then decreases as the number of items sold continues to increase beyond that point, confirming the function's shape and maximum profit point.