Chapter 13 Exercise 21, Introduction to Java Programming, Tenth Edition Y. Daniel LiangY.

13.21 (Algebra: vertex form equations)
The equation of a parabola can be expressed in either standard form
(y = ax^2 + bx + c) or vertex form (y = a(x - h)^2 + k).
Write a program that prompts the user to enter a, b, and c as integers
in standard form and displays h and k in the vertex form.

import java.math.BigDecimal;
import java.math.RoundingMode;

public class BigRational extends Number implements Comparable<BigRational> {
    // Data fields for numerator and denominator
    private BigDecimal numerator = BigDecimal.ZERO;
    private BigDecimal denominator = BigDecimal.ONE;

    /** Construct a rational with default properties */
    public BigRational() {
        this(BigDecimal.ZERO, BigDecimal.ONE);
    }

    /** Construct a rational with specified numerator and denominator */
    public BigRational(BigDecimal numerator, BigDecimal denominator) {
        BigDecimal gcd = gcd(numerator, denominator);
        this.numerator = ((denominator.compareTo(BigDecimal.ZERO) > 0) ? BigDecimal.ONE : new BigDecimal(-1)).multiply(numerator).divide(gcd);
        this.denominator = denominator.abs().divide(gcd);
    }

    public BigRational(String decimal) {

        int index = (decimal.contains(".")) ? decimal.indexOf('.') : decimal.indexOf('/');
        BigDecimal d;
        BigDecimal n;
        // if string is in decimal form
        if (decimal.contains(".")) {
            int power = decimal.substring(index + 1, decimal.length()).length();
            d = new BigDecimal(Math.pow(10,power));
            n = new BigDecimal(new StringBuilder(decimal).deleteCharAt(index).toString());
        } else {
            // if string contains '/'
            n = new BigDecimal(decimal.substring(0, index));
            d = new BigDecimal(decimal.substring(index + 1, decimal.length()));
        }

        BigDecimal gcd = gcd(n, d);
        this.numerator = ((d.compareTo(BigDecimal.ZERO) > 0) ? BigDecimal.ONE : new BigDecimal(-1)).multiply(n).divide(gcd);
        this.denominator = d.abs().divide(gcd);

    }

    /** Find GCD of two numbers */
    private static BigDecimal gcd(BigDecimal n, BigDecimal d) {
        BigDecimal n1 = n.abs();
        BigDecimal n2 = d.abs();

        BigDecimal remainder = n1.remainder(n2);
        while (remainder.compareTo(BigDecimal.ZERO) > 0) {
            n1 = n2;
            n2 = remainder;
            remainder = n1.remainder(n2);
        }




        return n2;
    }

    /** Return numerator */
    public BigDecimal getNumerator() {
        return numerator;
    }

    /** Return denominator */
    public BigDecimal getDenominator() {
        return denominator;
    }

    /** Add a rational number to this rational */
    public BigRational add(BigRational secondBigRational) {
        BigDecimal n1 = numerator.multiply(secondBigRational.getDenominator());
        BigDecimal n2 = denominator.multiply(secondBigRational.getNumerator());
        BigDecimal n = n1.add(n2);

        BigDecimal d = denominator.multiply(secondBigRational.getDenominator());
        return new BigRational(n, d);
    }

    /** Subtract a rational number from this rational */
    public BigRational subtract(BigRational secondBigRational) {
        BigDecimal n1 = numerator.multiply(secondBigRational.getDenominator());
        BigDecimal n2 = denominator.multiply(secondBigRational.getNumerator());
        BigDecimal n = n1.subtract(n2);

        BigDecimal d = denominator.multiply(secondBigRational.getDenominator());
        return new BigRational(n, d);
    }

    /** Multiply a rational number to this rational */
    public BigRational multiply(BigRational secondBigRational) {
        BigDecimal n = numerator.multiply(secondBigRational.getNumerator());
        BigDecimal d = denominator.multiply(secondBigRational.getDenominator());
        return new BigRational(n, d);
    }

    /** Divide a rational number from this rational */
    public BigRational divide(BigRational secondBigRational) {
        BigDecimal n = numerator.multiply(secondBigRational.getDenominator());
        BigDecimal d = denominator.multiply(secondBigRational.numerator);
        return new BigRational(n, d);
    }

    @Override
    public String toString() {
        if (denominator.equals(BigDecimal.ONE))
            return numerator + "";
       else
            return numerator + "/" + denominator;
    }

    @Override // Override the equals method in the Object class
    public boolean equals(Object other) {
        if ((this.subtract((BigRational)(other))).getNumerator().equals(BigDecimal.ZERO))
            return true;
        else
            return false;
    }

    @Override // Implement the abstract intValue method in Number
    public int intValue() {
        return (int)doubleValue();
    }

    @Override // Implement the abstract floatValue method in Number
    public float floatValue() {
        return (float)doubleValue();
    }

    @Override // Implement the doubleValue method in Number
    public double doubleValue() {
        return numerator.divide(denominator).doubleValue();
    }

    public BigDecimal bigDecimalDouble() {
        return numerator.divide(denominator, 100, RoundingMode.HALF_DOWN);
    }

    @Override // Implement the abstract longValue method in Number
    public long longValue() {
        return (long)doubleValue();
    }

    @Override // Implement the compareTo method in Comparable
    public int compareTo(BigRational o) {
        if (this.subtract(o).getNumerator().compareTo(BigDecimal.ZERO) > 0)
            return 1;
        else if (this.subtract(o).getNumerator().compareTo(BigDecimal.ZERO) < 0)
            return -1;
        else
            return 0;
    }
}

import java.util.Scanner;

public class Exercise_21 {

    public static void main(String[] args) {

        System.out.println("As integers..");
        System.out.print("Enter a, b, c: ");
        Scanner input = new Scanner(System.in);
        int a = input.nextInt();
        int b = input.nextInt();
        int c = input.nextInt();


        BigRational h = new BigRational(Double.toString((double)-b / (2 * a)));
        BigRational k = new BigRational(Double.toString(c - (Math.pow(b,2) / (4.0 * a))));
        System.out.println("h is " + h);
        System.out.println("k is " + k);


    }

}