Question

A company sells video games.

The amount of profil, y, that is
made by the company is related
to the selling price of each
video game, x. Given the
equation below, find the
maximum amount of profit, to the
nearest dollar.
y=-9x² +571x-3884

Answer 1

To find the maximum amount of profit, we need to find the vertex of the parabola defined by the quadratic equation.

The vertex form of a quadratic equation is:

y = a(x-h)^2 + k

Where (h,k) is the vertex of the parabola.

We can rewrite the given equation in vertex form by completing the square:

y = -9(x^2 - 63x) - 3884
= -9(x^2 - 63x + 729 - 729) - 3884
= -9(x-9)^2 - 3884

The maximum profit is -3884 dollars, to the nearest dollar.