Question 57210
Suppose that the equation p(x) = -2x^2 + 280x - 1000, where x represents the number of items sold, describes the profit function for a certain business. How many itmes should be sold to maximize the profit?
This is a parabolic function that opens down, its highest point is it's vertex.  This parabolic function is in standard form: {{{p(x)=ax^2+bx+c}}}. To find the x value of the vertex, use the formula: {{{x=-b/2a}}}
In your case, a=-2, b=280, and c=1000
The number of items that should be sold to maximize the profit is:
{{{x=-(280)/(2(-2))}}}
{{{x=-280/-4}}}
{{{highlight(x=70)}}}
Happy Calculating!!!