SOLUTION: The question is asking me to describe the meaning of the number -.2 in the formula P(x) = -.2x^2 + 120x - 12,500 where x is the number of items sold? I changed the numbers as I jus

Algebra ->  Graphs -> SOLUTION: The question is asking me to describe the meaning of the number -.2 in the formula P(x) = -.2x^2 + 120x - 12,500 where x is the number of items sold? I changed the numbers as I jus      Log On


   

Question 561145: The question is asking me to describe the meaning of the number -.2 in the formula P(x) = -.2x^2 + 120x - 12,500 where x is the number of items sold? I changed the numbers as I just want to know what steps to take to solve for the corrct answers.
Found 2 solutions by Theo, josmiceli:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
this is a quadratic equation.
the standard form of a quadratic equation is:
y = ax^2 + bx + c
when a is positive, the quadratic equation goes more positive on each end and has a minimum point in the middle.
when a is negative, the quadratic equation does more negative on each end and has a maximum point in the middle.
i'll make your equation even simpler for demonstration purposes.
assume your equation is y = -2x^2 + 5x - 3
the a term is equal to -2.
that's the coefficient of the x^2 term.
being negative, your quadratic equation will go more negative on both ends and will hit a maximum point in the middle.
the graph of your equation is shown below:
graph%28600%2C600%2C-5%2C5%2C-10%2C10%2C-2x%5E2%2B5x-3%29
if the coefficient of the x^2 term is positive, then the graph goes more positive at the ends and has a minimum point in the middle.
take your same equation and make the a term positive to get:
y = 2x^2 + 5x - 3
the graph of this equation is shown below:
graph%28600%2C600%2C-5%2C5%2C-10%2C10%2C2x%5E2%2B5x-3%29
that is the significance of the a term in your equation.
it's sign determines which way the quadratic equation is pointing.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The minus sign means that the curve has a maximum
and not a minimum.
As for the value, suppose I have +y+=+-2x%5E2+%2B+4x+%2B+1+
The plot is:
+graph%28+400%2C+400%2C+-5%2C+5%2C+-5%2C+5%2C+-2x%5E2+%2B+4x+%2B+1++%29+
Now If I change it to +y+=+-6x%5E2+%2B+4x+%2B+1+, the plot is
+graph%28+400%2C+400%2C+-5%2C+5%2C+-5%2C+5%2C+-6x%5E2+%2B+4x+%2B+1++%29+
This means a larger negative number would give you a
lower maximum profit and a smaller number of items
sold that will result in zero profit ( the x-intercept )