The relationship can be modeled by the quadratic equation p = - 100s^2 + 2400s - 8000, where p represents the profit and s represents the selling price. Which selling price will maximize profits? A.$12 B.$20 C.$8 D.$4

Question

Mathematics

Justice Ho

8 May, 08:16

The relationship can be modeled by the quadratic equation p = - 100s^2 + 2400s - 8000, where p represents the profit and s represents the selling price. Which selling price will maximize profits? A.$12 B.$20 C.$8 D.$4

+2

Answers (1)

Know the Answer?

Felipe Baker · Answer 1

A. $12

Step-by-step explanation:

For a quadratic of the form ax²+bx+c, the axis of symmetry is given by ...

x=-b / (2a)

For your quadratic function, the axis of symmetry is ...

s = - (2400) / (2 (-100)) = 12

The function has its extreme value on the axis of symmetry. Here, the leading coefficient is negative, so the parabola opens downward. That means the extreme value is a maximum.

Profit will be a maximum at a selling price of $12.