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

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) (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:

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:

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) (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
The plot is:

Now If I change it to , the plot is

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 )
RELATED QUESTIONS
Annual profit in thousands of dollars is given by the function, P(x) = 12x - 100, where x (answered by ewatrrr)
Annual profit in thousands of dollars is given by the function, P(x) = 12x - 100, where x (answered by josmiceli)
P(x) = 12x - 100 a. describe the meaning of the number -100 in the formula, in terms... (answered by mananth)
Annual profit in thousands of dollars is given by the function, P(x) = 12x - 100, where x (answered by josmiceli)
With the annual profit function p(x) = -.1^2 + 50x - 300, can you describe the meaning of (answered by josmiceli)
in the equation p(x)=12x-100 what is the meaning of the number 12 in the formula? what... (answered by stanbon)
The cost c(x) in dollars of producing x calculators is given c(x)=16000+120x and the... (answered by 303795)
I think I have my problem solved but would really like to verify my answers before... (answered by ewatrrr)
Annual profit in thousands of dollars is given by the function, P(x)= -.1x^2+50x-300,... (answered by Big Poop)