Public Class Form1

    Private a, b, c, d As Double
    Private paper As Graphics
    Private mypen As Pen = New Pen(Color.Black)

    Private Sub Form1_Load(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.Load
        TrackBar1.Minimum = -5
        TrackBar1.Maximum = 5
        TrackBar2.Minimum = -5
        TrackBar2.Maximum = 5
        TrackBar3.Minimum = -5
        TrackBar3.Maximum = 5
        TrackBar4.Minimum = -5
        TrackBar4.Maximum = 5
    End Sub

    Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click
        paper = PictureBox1.CreateGraphics()
        drawgraph()
    End Sub

    Private Sub TextBox1_TextChanged(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles TextBox1.TextChanged

    End Sub

    Private Sub TextBox2_TextChanged(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles TextBox2.TextChanged

    End Sub

    Private Sub TextBox3_TextChanged(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles TextBox3.TextChanged

    End Sub

    Private Sub TextBox4_TextChanged(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles TextBox4.TextChanged

    End Sub

    Private Sub PictureBox1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles PictureBox1.Click

    End Sub

    Private Sub Label1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Label1.Click

    End Sub

    Private Sub Label2_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Label2.Click

    End Sub

    Private Sub Label3_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Label3.Click

    End Sub

    Private Sub Label4_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Label4.Click

    End Sub

    Private Sub Draw()
        Dim x, y, nextX, nextY As Double
        Dim xPixel, yPixel, nextXPixel, nextYPixel As Integer
        For xPixel = 0 To PictureBox1.Width
            x = scaleX(xPixel)
            y = thefunction(x)
            yPixel = scaleY(y)
            nextXPixel = xPixel + 1
            nextX = scaleX(nextXPixel)
            nextY = thefunction(nextX)
            nextYPixel = scaleY(nextY)
            paper.DrawLine(mypen, xPixel, yPixel, nextXPixel, nextYPixel)
        Next
    End Sub

    Private Sub drawgraph()
        a = CDbl(TextBox1.Text)
        Label1.Text = "a = " & CStr(a)
        b = CDbl(TextBox2.Text)
        Label2.Text = "b = " & CStr(b)
        c = CDbl(TextBox3.Text)
        Label3.Text = "c = " & CStr(c)
        d = CDbl(TextBox4.Text)
        Label4.Text = "d = " & CStr(d)
        paper.Clear(Color.White)
        Draw()
    End Sub

    Private Function thefunction(ByVal x As Double) As Double
        'Return x * (x * (a * x + b) + c) + d
        Return Math.Log(x + 6.0)
    End Function
    Private Function scaleX(ByVal xPixel As Integer) As Double
        Dim xStart As Double = -5, xEnd As Double = 5
        Dim xScale As Double = PictureBox1.Width / (xEnd - xStart)
        Return (xPixel - (PictureBox1.Width / 2)) / xScale
    End Function
    Private Function scaleY(ByVal y As Double) As Integer
        Dim yStart As Double = -5, yEnd As Double = 5
        Dim pixelCoord As Integer
        Dim yScale As Double = PictureBox1.Height / (yEnd - yStart)
        pixelCoord = CInt(-y * yScale) + _
        CInt(PictureBox1.Height / 2)
        Return pixelCoord
    End Function

    Private Sub TrackBar1_Scroll(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles TrackBar1.Scroll
        TextBox1.Text = TrackBar1.Value
        paper = PictureBox1.CreateGraphics()
        drawgraph()
    End Sub

    Private Sub TrackBar2_Scroll(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles TrackBar2.Scroll
        TextBox2.Text = TrackBar2.Value
        paper = PictureBox1.CreateGraphics()
        drawgraph()

    End Sub

    Private Sub TrackBar3_Scroll(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles TrackBar3.Scroll
        TextBox3.Text = TrackBar3.Value

        paper = PictureBox1.CreateGraphics()
        drawgraph()
    End Sub

    Private Sub TrackBar4_Scroll(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles TrackBar4.Scroll
        TextBox4.Text = TrackBar4.Value
        paper = PictureBox1.CreateGraphics()
        drawgraph()
    End Sub
End Class