Factorizing Quadratic Equations (practice and solver)

Article
1/17/2024

Overview

There are several different methods for solving Quadratic equations. This application focuses on solving by Factorizing.

The application is primarily a revision aid, being comprised of a practice app. and a solver app.

**Figure 1. Manually solving practice questions.
**

**Figure 2. Solving programmatically.
**

The program consists of one Form and two UserControls:

The bracket UC is a dual purpose control...:

...and is shown in Figure 1, where it is used for input, and in Figure 2 (the lower control) in readonly mode as an output control.

The equation UC...:

...is an input control which can be seen in Figure 2 (the top control).

The code – The bracket UC

Both the bracket control (in input mode) and the equation control are restricted in the input they will accept. I haven’t included the input restricting code here.

The code includes a Boolean [readonly] Property and four String Properties for retrieving and setting text in the Labels and TextBoxes. The Paint event is handled to draw highlighting lines below the TextBoxes.

This UC also has two Public methods, alignControls which moves the controls to accommodate different text, and reset which resets the control’s text back to the default values.

Public Class bracket

    Private _readonly As Boolean = False
  Public Property [readonly]() As Boolean
  Get
  Return _readonly
  End Get
  Set(ByVal value As Boolean)
_readonly = value
TextBox1.ReadOnly = value
TextBox2.ReadOnly = value
  End Set
  End Property

    Public Property a1() As String
  Get
  Return Label1.Text
  End Get
  Set(ByVal value As String)
Label1.Text = value
  End Set
  End Property

    Public Property a2() As String
  Get
  Return Label4.Text
  End Get
  Set(ByVal value As String)
Label4.Text = value
  End Set
  End Property

    Public Property i1() As String
  Get
  Return TextBox1.Text
  End Get
  Set(ByVal value As String)
TextBox1.Text = value
  End Set
  End Property

    Public Property i2() As String
  Get
  Return TextBox2.Text
  End Get
  Set(ByVal value As String)
TextBox2.Text = value
  End Set
  End Property

Private Sub bracket_Paint(ByVal sender As Object, ByVal e As System.Windows.Forms.PaintEventArgs) Handles Me.Paint
e.Graphics.DrawLine(Pens.Black, TextBox1.Left - 1, TextBox1.Bottom - 4, TextBox1.Left - 1, TextBox1.Bottom + 1)
e.Graphics.DrawLine(Pens.Black, TextBox1.Left - 1, TextBox1.Bottom + 1, TextBox1.Right + 1, TextBox1.Bottom + 1)
e.Graphics.DrawLine(Pens.Black, TextBox1.Right + 1, TextBox1.Bottom - 4, TextBox1.Right + 1, TextBox1.Bottom + 1)
e.Graphics.DrawLine(Pens.Black, TextBox2.Left - 1, TextBox2.Bottom - 4, TextBox2.Left - 1, TextBox2.Bottom + 1)
e.Graphics.DrawLine(Pens.Black, TextBox2.Left - 1, TextBox2.Bottom + 1, TextBox2.Right + 1, TextBox2.Bottom + 1)
e.Graphics.DrawLine(Pens.Black, TextBox2.Right + 1, TextBox2.Bottom - 4, TextBox2.Right + 1, TextBox2.Bottom + 1)
End Sub

    Public Sub alignControls()
TextBox1.Left = Label1.Right + 6
Label2.Left = TextBox1.Right + 6
Label4.Left = Label2.Right - 2
TextBox2.Left = Label4.Right + 6
Label3.Left = TextBox2.Right + 6
  Me.Invalidate()
  End Sub

    Public Sub reset()
Label1.Text = "(x"
Label4.Text = "(x"
TextBox1.Clear()
TextBox2.Clear()
  End Sub

The code – The equation UC

This UC has three String Properties, which expose the TextBoxes’ Text Properties. It also contains a Public reset method which resets the input control’s text back to the default values.

Public Class equation

Public Sub reset()
TextBox1.Clear()
TextBox2.Clear()
TextBox3.Clear()
End Sub

    Public Property a() As String
  Get
  Return TextBox1.Text
  End Get
  Set(ByVal value As String)
TextBox1.Text = value
  End Set
  End Property

    Public Property b() As String
  Get
  Return TextBox2.Text
  End Get
  Set(ByVal value As String)
TextBox2.Text = value
  End Set
  End Property

    Public Property c() As String
  Get
  Return TextBox3.Text
  End Get
  Set(ByVal value As String)
TextBox3.Text = value
  End Set
  End Property

End Class

The code – The Form

The Form code is organized into five distinct regions:

Ø common variables

These are Form level and used by the practice part of the application.

      Dim a As Integer

  Dim b As Integer

  Dim c As Integer

  Dim r As New Random

      Dim i1 As Integer

  Dim i2 As Integer



  Dim solutions As String = ""

Ø practise

The practice part of the application formulates random equations, and checks your answers.

Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click

Label4.Text = ""

            Dim a1 As Integer

  Dim a2 As Integer

a1 = r.Next(-9, 13)

a2 = r.Next(-9, 13)

a = a1 * a2

  While a = 0

a1 = r.Next(-9, 13)

a2 = r.Next(-9, 13)

a = a1 * a2

  End While

            Do

i1 = r.Next(-9, 13)

i2 = r.Next(-9, 13)

b = a1 * i2 + i1 * a2

c = i1 * i2

  Loop While b = 0 Or c = 0

            '(3x - 2)(x + 3)

      Label3.Text = String.Format("Solve:{0}{1}x² {2}x {3} = 0", Environment.NewLine, a, If(b > 0, "+" & b.ToString, b.ToString), If(c > 0, "+" & c.ToString, c.ToString))

   Bracket1.a1 = String.Format("({0}x", If(a1 = 1, "", a1.ToString))

Bracket1.a2 = String.Format("({0}x", If(a2 = 1, "", a2.ToString))

Bracket1.i1 = ""

Bracket1.i2 = ""

Bracket1.alignControls()

            solutions = String.Format("x = {0} or x = {1}", simplify(i1, a1), simplify(i2, a2))

    End Sub

    Private Sub Button2_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button2.Click

            Dim int1, int2 As Integer

            If Integer.TryParse(Bracket1.i1.TrimStart("+"c), int1) AndAlso Integer.TryParse(Bracket1.i2.TrimStart("+"c), int2) Then

  If i1 = int1 AndAlso i2 = int2 Then

MsgBox("Correct answer", MsgBoxStyle.Information)

Label4.Text = solutions

  Else

MsgBox("Try again", MsgBoxStyle.Exclamation)

  End If

End If

  End Sub

Ø solve

The solve part of the application allows you to specify a Quadratic Equation and programmatically solve that equation.

Private Sub Button3_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button3.Click

            Bracket2.reset()

Label5.Text = ""

            Dim quadratic, linear, constant As Integer

  If Integer.TryParse(Equation1.a, quadratic) AndAlso Integer.TryParse(Equation1.b, linear) AndAlso Integer.TryParse(Equation1.c, constant) Then

                  Dim aDivisors As List(Of Point) = getDivisors(quadratic)

  Dim cDivisors As List(Of Point) = getDivisors(constant)

                  '(3x - 2)(x + 3)

  For x1 As Integer = aDivisors.Count - 1 To 0 Step -1

  For x2 As Integer = 0 To cDivisors.Count - 1

  If aDivisors(x1).X * cDivisors(x2).Y + cDivisors(x2).X * aDivisors(x1).Y = linear Then

Bracket2.a1 = String.Format("({0}x", If(aDivisors(x1).X = 1, "", aDivisors(x1).X.ToString))

Bracket2.a2 = String.Format("({0}x", If(aDivisors(x1).Y = 1, "", aDivisors(x1).Y.ToString))

Bracket2.i1 = If(cDivisors(x2).X > 0, "+" & cDivisors(x2).X.ToString, cDivisors(x2).X.ToString)

Bracket2.i2 = If(cDivisors(x2).Y > 0, "+" & cDivisors(x2).Y.ToString, cDivisors(x2).Y.ToString)

Bracket2.alignControls()

Label5.Text = String.Format("x = {0} or x = {1}", simplify(cDivisors(x2).X, aDivisors(x1).X), simplify(cDivisors(x2).Y, aDivisors(x1).Y))

  Return

  End If

  Next

  Next

  End If

  End Sub

    Private Function getDivisors(ByVal x As Integer) As List(Of Point)

  Dim divisors As New List(Of Point)(Enumerable.Range(If(x > 0, -x, x), Math.Abs(x) * 2).Except(New Integer() {0}).Where(Function(n) x Mod n = 0).Select(Function(n) New Point(n, (x \ n))).ToArray)

  Return divisors

  End Function

    Private Sub Button4_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button4.Click

            Bracket2.reset()

Equation1.reset()

Label5.Text = ""

End Sub

Ø common methods

Common methods contains just one Function which is used for simplifying fractions.

Private Function simplify(ByVal n As Integer, ByVal d As Integer) As String

            If d = 1 Or d = -1 Then Return n.ToString

  Dim hcd As Integer = Enumerable.Range(2, Math.Max(Math.Abs(n), Math.Abs(d))).LastOrDefault(Function(x) n Mod x = 0 AndAlso d Mod x = 0)

  If hcd > 0 Then

n \ hcd

d \ hcd

                  If d = 1 Or d = -1 And n < 0 Then

  Return (n \ d).ToString

  ElseIf d = -1 And n > 0 Then

  Return "-" & (n \ d).ToString

  End If

                  Return String.Format("{2}{0}/{1}", Math.Abs(n), Math.Abs(d), If((n / d) < 0, "-", ""))

  Else

  Return String.Format("{2}{0}/{1}", Math.Abs(n), Math.Abs(d), If((n / d) < 0, "-", ""))

  End If

  Return ""

End Function



Ø form

The general Form code handles the TabPage Paint events and adds some extra functionality to the application.

Private Sub Form1_KeyDown(ByVal sender As Object, ByVal e As System.Windows.Forms.KeyEventArgs) Handles Me.KeyDown

            If e.KeyCode = Keys.F2 Then

  If TabControl1.SelectedIndex = 0 Then

MsgBox(String.Format("{0}, {1}", i1, i2))

  End If

  ElseIf e.KeyCode = Keys.F3 Then

  If TabControl1.SelectedIndex = 0 Then

TabControl1.SelectedIndex = 1

Bracket2.reset()

Equation1.reset()

Equation1.a = a.ToString

Equation1.b = If(b > 0, "+" & b.ToString, b.ToString)

Equation1.c = If(c > 0, "+" & c.ToString, c.ToString)

  End If

  End If

  End Sub

    Private Sub Form1_Load(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.Load

            TabControl1.SelectedIndex = 0

Button1.PerformClick()

  Me.KeyPreview = True

  End Sub

    Private Sub TabPage1_Paint(ByVal sender As Object, ByVal e As System.Windows.Forms.PaintEventArgs) Handles TabPage1.Paint

  For c As Integer = 0 To Me.Width Step 25

e.Graphics.DrawLine(Pens.LightGray, c, 0, c, Me.Height)

  Next


  For r As Integer = 0 To Me.Height Step 25

e.Graphics.DrawLine(Pens.LightGray, 0, r, Me.Width, r)

  Next

  End Sub

    Private Sub TabPage2_Paint(ByVal sender As Object, ByVal e As System.Windows.Forms.PaintEventArgs) Handles TabPage2.Paint

  For c As Integer = 0 To Me.Width Step 25

e.Graphics.DrawLine(Pens.LightGray, c, 0, c, Me.Height)

  Next

  For r As Integer = 0 To Me.Height Step 25

e.Graphics.DrawLine(Pens.LightGray, 0, r, Me.Width, r)

  Next

  End Sub

    Private Sub TextBox1_KeyDown(ByVal sender As Object, ByVal e As System.Windows.Forms.KeyEventArgs) Handles TextBox1.KeyDown

  If e.KeyCode = Keys.Up Then

TextBox1.SelectedText = "²"

  End If

End Sub

Share via

Factorizing Quadratic Equations (practice and solver)

Overview

The code – The bracket UC

The code – The equation UC

The code – The Form

See Also

Additional resources

Share via

Factorizing Quadratic Equations (practice and solver)

Overview

The code – The bracket UC

The code – The equation UC

The code – The Form

**See Also **

Additional resources

See Also