Question 57213
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 quadratic equation that results in a parabola when graphed.  Because x^2 is negative the parabola is upside down and "n" shaped.  It's vertex is its maximum point.
We find the x value of a quadratic equation in standard form:{{{p(x)=ax^2+bx+c}}} with the formula: {{{highlight(x=-b/2a)}}}
Our a=-2 and b=280
{{{x=-(280)/(2(-2))}}}
{{{x=-280/-4}}}
{{{x=70}}}
The company must sell 70 items to maximize the profit.
Happy Calculating!!!