public class Quadratic {
  // three double instance variables representing a, b, and c.
  double a, b, c;
  
  // Constructor that takes three double parameters representing a, b, and c.
  public Quadratic(double a$, double b$, double c$) {
  }
  
  
  // Constructor that copies a Quadratic
  public Quadratic(Quadratic q) {
  }
  
  
  
  // printable form of this quadratic
  public String toString() {
    return "0 x^2 + 0 x + 0";
  }
  
  
  // returns a double representing quadratic function evaluated at x.
  public double f(double x) {
    return 0.0;
  }
  
  
  // returns the discriminant of this quadratic: (b^2 - 4 a c)
  public double discriminant() {
    return 0.0;
  }
  
  
  // returns a boolean that is true if the graph of the quadratic opens up
  public boolean concaveUp() {
    return false;
  }
  
  
  // returns a boolean that is true if the graph of the quadratic opens down
  public boolean concaveDown() {
    return false;
  }
  
  
  // returns an int that represents the number of real roots of this quadratic
  // 0 - both roots are complex when the discriminant is negative
  // 1 - both roots are equal and real when the discriminant is zero
  // 2 - both roots are real an distinct when the discriminant is positive
  public int realRootCount() {
    return 0;
  }
  
  
  // returns a Complex value that represents the first root of the polynomial
  // Hint: Use the discriminant and realRootCount functions
  public Complex root1() {
    return new Complex(0.0D, 0.0D);
  }
  
  
  // returns a Complex value that represents the first root of the polynomial
  // Hint: Use the discriminant and realRootCount functions
  public Complex root2() {
    return new Complex(0.0D, 0.0D);
  }
  
  
  // returns a Point2D representing the vetex of the parabola
  // Recall that the vertex of the parablola is given by (-b/(2a), f(-b/(2a)))
  public Point2D vertex() {
    return new Point2D(0.0, 0.0);
  }
  
  
  // returns a double that is the insantaneous slope of this Quadratic at x: 2 a x + b
  public double slope(double x) {
    return 0.0;
  }
  
  
  // returns a line that represents the derivative of this Quadratic at x
  // 2 a x + b is the slope
  // (x, f(x)) is a point on the line
  // Use point-slope equation to determine the y intercept
  public Line derivative(double x) {
    return new Line(0.0, 0.0);
  }
  
  
  // integral-ish helper method
  // Define F(x) = (a/3)x^3 + (b/2)x^2 + c x 
  double F(double x) {
    return 0.0;
  }
  
  
  // returns a double representing the definite integral from x1 < x2 of this quadratic.
  // intgrate(x1,x2) returns F(x2) - F(x1). 
  public double integrate(double x1, double x2) {
    return 0.0;
  }
  
  public static void main(String args[]) {
    Quadratic q1 = new Quadratic(1, -5, 6);
    System.out.println(q1); // 1.0 x^2 + -5.0 x + 6.0 
    System.out.println(q1.concaveUp()); // true
    System.out.println(q1.concaveDown());  // false
    System.out.println(q1.f(0)); // 6
    System.out.println(q1.f(3)); // 0
    System.out.println(q1.f(2)); // 0
    System.out.println(q1.vertex());  // (2.5, -0.25)
    System.out.println(q1.f(q1.vertex().x));  // -0.25
    System.out.println(q1.slope(4));  // 3
    System.out.println(q1.integrate(0,2));  // 4.66666666
    System.out.println(q1.discriminant());  // 1.0
    System.out.println(q1.realRootCount());  // 2
    System.out.println(q1.root1());  // 3.0
    System.out.println(q1.root2());  // 2.0
    System.out.println(q1.derivative(1)); // y = -3.0 x + 5.0 
    
    System.out.println("- - - - - - - - - - - - - - - - -");
    
    Quadratic q2 = new Quadratic(-1,-2,-3);
    System.out.println(q2); // -1.0 x^2 + -2.0 x + -3.0  
    System.out.println(q2.concaveUp()); // false
    System.out.println(q2.concaveDown());  // true
    System.out.println(q2.f(0)); // -3
    System.out.println(q2.f(3)); // -18
    System.out.println(q2.f(2)); // -11
    System.out.println(q2.vertex());  // (-1,-2)
    System.out.println(q2.f(q2.vertex().x));  // -2
    System.out.println(q2.slope(4));  // -10
    System.out.println(q2.integrate(0,2));  // -12.66666666
    System.out.println(q2.discriminant());  // -8
    System.out.println(q2.root1());  // -1.0+1.4142135623730951i
    System.out.println(q2.root2());  // -1.0-1.4142135623730951i
    System.out.println(q1.realRootCount());  // 2
    System.out.println(q2.derivative(1)); // y = -4.0 x + -2.0 
  }
}