SOLUTION: 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 so

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Question 57213This question is from textbook
: 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 question is from textbook

Answer by funmath(2933) About Me  (Show Source):
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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%28x%29=ax%5E2%2Bbx%2Bc with the formula: highlight%28x=-b%2F2a%29
Our a=-2 and b=280
x=-%28280%29%2F%282%28-2%29%29
x=-280%2F-4
x=70
The company must sell 70 items to maximize the profit.
Happy Calculating!!!