after research a software company determined the function below to represent the total profit in dollars from the sales of x items
P(x)=-25x^2+48,750x-50,000
describes the symmetry of the function.
The given function P(x) is a quadratic function, so it is a symmetric about its vertical line of symmetry.
To find the vertical line of symmetry of the function, we can use the formula x = -b/(2a), where the function is in the form of ax^2 + bx + c.
In this case, a = -25 and b = 48,750. Plugging these values into the formula, we get:
x = -48,750 / (2*(-25))
x = -48,750 / (-50)
x = 975
Therefore, the vertical line of symmetry of the function is x = 975. This means the graph of the function is symmetric about the vertical line x = 975.