Determining Parabola from Three Points

Just like two points uniquely defines a line, I realized that three points uniquely defines a parabola. It's fun to determine the equation from the three points and sometimes I'd use this method on homeworks/tests instead of memorizing other formulas, because I found this much more intuitive..

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Sample input:

-1.0
-3.0
-4.0
5.0
-2.0x^2 +5.0x +1.0

import java.awt.Point;
import java.awt.geom.Point2D;


public class determineParabolaFromThreePoints {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub

		
		//make sure the points are in descending x order
		Point one = new Point (0,1); 
		Point two = new Point (3,-2);
		Point three = new Point (1,4);
		
		
		//calculate two slopes
		double yslopea = (two.getY()-one.getY())/(two.getX()-one.getX());
		System.out.println(yslopea);
		double yslopeb = (three.getY()-two.getY())/(three.getX()-two.getX());
		System.out.println(yslopeb);
		
		//calculate the x values of those slopes, we can do this because 
		//we know concavity is a constant for the entire domain
		double xslopea = (one.getX()+two.getX())/2;
		double xslopeb = (two.getX()+three.getX())/2;
		
		//calculate a constant of concavity 
		double concavity = (yslopeb-yslopea)/(xslopeb-xslopea);
		System.out.println(concavity);
		
		//now that we know concavity, we calculate the slope at point one
		double slopeAtOne = yslopea-((xslopea-one.getX())*concavity);
		System.out.println(slopeAtOne);
		
		
		//because we know the equation is of the form ax^2 + bx + c
		//we know its derivative is 2ax + b 
		//we know its second derivative is 2a, so we set 2a = concavity and solve for a 
		
		double a = (concavity/2);
		double b=(-2*one.getX()*a)+slopeAtOne;
		double c=((-a*(one.getX()*one.getX()))-(b*one.getX()))+one.getY();
		
	
		
		if(c==0&&b==0){
			System.out.println(a+"x^2");
		}
		
		if(c==0&&b!=0){
		System.out.println(a+"x^2 +"+b+"x");
		}
		
		if(c!=0&&b==0){
			System.out.println(a+"x^2 +"+c);
			}
		if(c!=0&&b!=0){
			System.out.println(a+"x^2 +"+b+"x +"+c);
			}
		}

}