Question 764740: Suppose that the equation p(x) = -4x2 + 400x - 1000, where x represents the number of items sold, describes the profit function for a certain business. How many items should be sold to maximize the profit?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! WITHOUT MEMORIZED FORMULAS OR NAMES:
The function  can be re-written in a form that gives you a better understanding (and the answer to the problem.
-->  -->  --> 
When  the firt term is zero 
and  .
For any other value of  ,  and  ,
so is the number of items sold that maximizes the profit,
and  is the maximum profit possible.
WITH WORDS AND FORMULAS TO MEMORIZE:
is a  function (meaning a polynomial of degree 2).
A quadratic function, like 
graphs as a  and has a maximum or a minimum (the  of the parabola).
If the leading coefficient is negative, the function has a maximum. Otherwise, it's a minimum.
Quadratic functions are of the form 
(or  when in vertex form).
The number you want to find is  , the x-coordinate of the vertex of the parabola, which is part of
 , the equation of the axis of symmetry of the parabola.
If your teacher insist on memorization of formulas, you may have to memorize  , and for your problem you would write
 ,  -->  --> 
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