Parabola as object

Make a class defining a polynomial of second degree y = A× x² + B× x + C

The coefficients A, B, C should be private. The class should contain the following member functions:

• a function that sets the coefficients to desired values
• a function that calculates y for a given value of x
• a function that tells how many roots there are and returns the roots (if any)
• a function that tells whether the polynomial has a maximum, a minimum, or no extremum, and gives x and y for the extremum (if any)

Make a program to test an object of this class.

In case you've forgotten everything you've learned in math, here are the formulae:

Discriminant