Question

ASAP

(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. Hint: Use the Rational class in LiveExample 13.13 for computing h and k. Use the template at https://liveexample.pearsoncmg.com/test/Exercise13_21Test.txt for your code. Sample Run 1 Enter a, b, c: 1 3 1 h is -3/2 k is -5/4 Sample Run 2 Enter a, b, c: 2 3 4 h is -3/4 k is 23/8 Class Name: Exercise13_21 If you get a logical or runtime error, please refer https://liveexample.pearsoncmg.com/faq.html.

Answer 1

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package com.company;
import java.util.Scanner;

public class Exercise13_21 {
    static Scanner sc =  new Scanner(System.in);
    public static void main(String[] args) {
        System.out.println("Enter the Coefficients");
        System.out.println("Enter a:");
        int a = sc.nextInt();
        System.out.println("Enter b:");
        int b = sc.nextInt();
        System.out.println("Enter c:");
        int c = sc.nextInt();
        //so we need to compute 'h' which is -b/(2*a)
        Rational h =  new Rational((-1)*b,2*a);
        //finding k
        Rational hsquare = new Rational(h.multiply(h).getNumerator(),h.multiply(h).getDenominator());
        Rational first = new Rational(hsquare.multiply(new Rational(a,1)).getNumerator(),hsquare.multiply(new Rational(a,1)).getDenominator());
        Rational second = h.multiply(new Rational(b,1));
        Rational finalAnswer = first.add(second).add(new Rational(c,1));

        System.out.println("Vertex form: h,k"+h+" and k is "+finalAnswer);

    }
}


// Copy from the book
class Rational extends Number implements Comparable<Rational> {
    // Data fields for numerator and denominator
    private long numerator = 0;
    private long denominator = 1;

    /** Construct a rational with default properties */
    public Rational() {
        this(0, 1);
    }

    /** Construct a rational with specified numerator and denominator */
    public Rational(long numerator, long denominator) {
        long gcd = gcd(numerator, denominator);
        this.numerator = (denominator > 0 ? 1 : -1) * numerator / gcd;
        this.denominator = Math.abs(denominator) / gcd;
    }

    /** Find GCD of two numbers */
    private static long gcd(long n, long d) {
        long n1 = Math.abs(n);
        long n2 = Math.abs(d);
        int gcd = 1;

        for (int k = 1; k <= n1 && k <= n2; k++) {
            if (n1 % k == 0 && n2 % k == 0)
                gcd = k;
        }

        return gcd;
    }

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

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

    /** Add a rational number to this rational */
    public Rational add(Rational secondRational) {
        long n = numerator * secondRational.getDenominator() +
                denominator * secondRational.getNumerator();
        long d = denominator * secondRational.getDenominator();
        return new Rational(n, d);
    }

    /** Subtract a rational number from this rational */
    public Rational subtract(Rational secondRational) {
        long n = numerator * secondRational.getDenominator()
                - denominator * secondRational.getNumerator();
        long d = denominator * secondRational.getDenominator();
        return new Rational(n, d);
    }

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

    /** Divide a rational number from this rational */
    public Rational divide(Rational secondRational) {
        long n = numerator * secondRational.getDenominator();
        long d = denominator * secondRational.numerator;
        return new Rational(n, d);
    }

    @Override
    public String toString() {
        if (denominator == 1)
            return numerator + "";
        else
            return numerator + "/" + denominator;
    }

    @Override // Override the equals method in the Object class
    public boolean equals(Object other) {
        if ((this.subtract((Rational)(other))).getNumerator() == 0)
            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 * 1.0 / denominator;
    }

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

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

Sample output: