//
// This example demonstrates overloading of the function call operator,
// aka  operator() , to create quadratic functions.
//
// Consider functions  f(x) = a x^2 + b x + c .

#include <iostream.h>

class Quadratic {
private:
  double coeff[3];

public:
  Quadratic() {                          // default -- zero function
    coeff[0] = coeff[1] = coeff[2] = 0;
  }
  Quadratic( double a, double b, double c ) {
    coeff[2] = a;  // coefficients are numbered by degree of x
    coeff[1] = b;  
    coeff[0] = c;
  }  

  // implement evaluation of a function (aka "plugging in the x")

  double operator() ( double x ){
    return ( coeff[2]*x*x + coeff[1]*x + coeff[0] );
  }
};     
 
// run this test to be sure ...
// Question: what happens on assignment of Quadratics?
//           E.g.    Quadratic f1( 2, 6, -5 ), f2;
//                   f2 = f1;                          
//           what is inside f2 now?

int main(){
  Quadratic f( 1, -2, 1) ;    // construct x^2 - 2x + 1
  Quadratic g( 1, 5, 6 ) ;    // construct x^2 + 5x + 6
  Quadratic h( 4, 0, -9) ;    // construct 4x^2 - 9

  cout << "For f(x) = x^2 - 2x + 1 \n";
  for( double x = -5; x <= 5 ; x += 0.5 ) {
    cout << "f(" << x << ")= "; 
    cout << f(x) << endl;              // notice that f is NOT a function 
  }
  cout << endl << endl;

  cout << "For g(x) = x^2 + 5x + 6 \n";
  for( double x = -5; x <= 5 ; x += 0.5 ) {
    cout << "g(" << x << ")= "; 
    cout << g(x) << endl;              // notice that g is NOT a function 
  }
  cout << endl << endl;

  cout << "For h(x) = 4x^2 - 9 \n";
  for( double x = -5; x <= 5 ; x += 0.5 ) {
    cout << "h(" << x << ")= "; 
    cout << h(x) << endl;              // notice that h is NOT a function 
  }
  cout << "\nDone.\n";
}