Understanding the Quadratic Function | Maths Explanation for VB.Net Kids
In this tutorial, we'll explore how to solve quadratic equations in VB.Net and use them to plot and animate a quadratic curve on a VB.Net windows form. Understanding the quadratic equation in programming helps you create parabolic motion, simulations, and engaging math visuals.
A quadratic equation has the general form y = ax2 + bx + c; where a, b, and c are constants. This tutorial explains how to solve, plot, and animate a quadratic function using VB.Net and the VB.Net windows form.
Generating Quadratic Curves for VB.Net
To generate a quadratic curve in VB.Net, you need two points - the starting point and the vertex (turning point - maximum or minimum).
The general quadratic function is:
y = ax2 + bx + c
dy/dx = yI = 2ax + b
At maximum / minimum point, yI = 0
yI|(x = xmax) = 0
2axmax + b = 0
b = -2axmax
Substituting b in the general equation
y = ax2 + bx + c
= ax2 - 2axmaxx + c
At (xstart, ystart):
ystart = axstart2 - 2axmaxxstart + c
At (xmax, ymax):
ymax = axmax2 - 2axmax2 + c
= -axmax2 + c
--------- (eqn *)
Subtracting both derived equations
ystart - ymax =
axstart2 - 2axmaxxstart
+ axmax2
(xstart2 - 2xmaxxstart
+ xmax2)a = ystart - ymax
| a = | ystart - ymax | = | ystart - ymax |
| xstart2 - 2xmaxxstart + xmax2 | (xstart - xmax)2 |
b = -2axmax
& from (eqn *)
c = ymax + axmax2
VB.Net Code Example: Quadratic Path Animation
Once we have the equation, we can generate a quadratic curve with VB.Net to visualize its motion. The following example demonstrates how to animate an object along a quadratic curve in VB.Net using the VB.Net windows form. This is a simple form of quadratic motion simulation that helps visualize parabolic motion, such as a ball being thrown.
To make a body travel by the equation of a quadratic curve, continuously increment x by some interval, and use the quadratic equation to get the corresponding y value.
Create a new Visual Basic Windows Forms Application
project
;
call it Dymetric_VB.
Create 3 new VB.Net classes;
Call them Facet, Dymetric and QuadraticPath.
Type out the adjoining VB.Net code for animating an image body through
the path of a quadratic curve.
This simple example demonstrates VB.Net quadratic animation.
Key Takeaways on Quadratic Path Animation in VB.Net
- A quadratic function in VB.Net models parabolic motion or curves.
- The quadratic equation VB.Net code can be used for plotting and animations.
- The constants a, b, and c control the shape and direction of the parabola.
Applications in Programming and Education
The quadratic equation in VB.Net is useful for programming concepts like projectile motion, trajectory planning, and smooth animation curves. Teachers can use this example to show how maths and coding connect - making parabolas come alive through VB.Net programming.
Teachers and students can use this VB.Net quadratic formula tutorial to explore math and programming together. It's a practical example of using maths with code.
Summary: Visualizing Quadratic Equations in VB.Net
In this tutorial, you've learnt how to solve quadratic equations in VB.Net using the quadratic formula. We've also explore how to plot and animate a quadratic curve on a VB.Net windows form. Understanding how to code the quadratic equation in VB.Net is useful for creating simulations, parabolic motion, and smooth animations.
By combining mathematics and VB.Net, you can solve and animate quadratic equations easily. Whether you're plotting parabolas, simulating motion, or building educational tools, mastering the quadratic formula in VB.Net gives you a solid foundation in computational math.
So! VB.Net Fun Practice Exercise - Animate along Quadratic Path
As a fun practice exercise, try adjusting the coefficients a, b,
and c to change the curve's shape or motion pattern.
This will be a great way to connect mathematics and programming, and help you
understand more about VB.Net animations and quadratic equations.
VB.Net Quadratic Path Window Display Code Stub
Private form_details As New Facet
Private action_class As New Dymetric
Private Sub Form1_Load(sender As Object, e As EventArgs) Handles MyBase.Load
' Fill in Form - Put button on form
form_details.formFeatures(sender)
End Sub
Private Sub Form1_Paint(sender As Object, e As PaintEventArgs) Handles Me.Paint
' Colour button area
form_details.decorateButtonArea(sender, e)
' Call MovingBody class into action
action_class.decideAction(sender, Me.CreateGraphics(), form_details.CLICK_OCCURRED)
' Reset click variable
form_details.CLICK_OCCURRED = False
End Sub
End Class
VB.Net Quadratic Path Facet Window Code Stub
Dim screen_rect As Rectangle
Public CLICK_OCCURRED As Boolean = False
Public Sub formFeatures(sender As Object)
'Set window position, width and height
screen_rect = Screen.PrimaryScreen.Bounds
sender.SetDesktopBounds(0, 0, screen_rect.Width, screen_rect.Height)
' Set a display text
sender.Text = "useOfMaths.com"
' Set a background colour
sender.BackColor = System.Drawing.Color.LightGray
' Set an icon image
Dim path = System.IO.Path.GetDirectoryName(System.Reflection.Assembly.GetExecutingAssembly().CodeBase)
path = New Uri(path).LocalPath
Try
sender.Icon = New Icon(path & "\useOfMaths.ico")
Catch ex As System.IO.FileNotFoundException
' Well, just go on and use default pic
End Try
'
'create a button - response_btn
'
Dim response_btn As New Button()
response_btn.BackColor = System.Drawing.Color.Magenta
response_btn.ForeColor = System.Drawing.Color.Blue
response_btn.Name = "response_btn"
response_btn.SetBounds(CInt(Math.Round(screen_rect.Width / 2)) - 50, 5, 100, 40)
response_btn.Text = "Move"
sender.Controls.Add(response_btn)
AddHandler response_btn.Click, AddressOf response_btn_Click
End Sub
Public Sub decorateButtonArea(sender As Object, e As PaintEventArgs)
' Draw a dotted line
Dim pencil As New System.Drawing.Pen(System.Drawing.Color.Black)
pencil.DashStyle = Drawing2D.DashStyle.DashDot
pencil.Width = 5
e.Graphics.DrawLine(pencil, 0, 50, sender.Width, 50)
pencil.Dispose()
' Colour region
Dim paint_brush As New System.Drawing.SolidBrush(System.Drawing.Color.Pink)
e.Graphics.FillRectangle(paint_brush, 0, 0, sender.Width, 50)
paint_brush.Dispose()
End Sub
Public Sub response_btn_Click(sender As Object, e As EventArgs)
' turn this on on every button click
CLICK_OCCURRED = True
sender.Refresh()
End Sub
End Class
VB.Net Quadratic Path Code for Dymetric Class
Private quad_curve As New QuadraticPath
Private do_simulation = False
' decide what course of action to take
Public Sub decideAction(sender As Object, g As Graphics, click_check As Boolean)
If do_simulation And click_check Then
' do animation
quad_curve.play(sender, g)
do_simulation = False
Else
' Put ball on screen
quad_curve.prep(sender, g)
do_simulation = True
End If
End Sub
End Class
VB.Net Animation Code for Quadratic Path Class
Private x_start, y_start, x_max, y_max, x, y As Integer
Private a, b, c As Double
Private Const dotDIAMETER = 10
Dim dot_colour As New System.Drawing.SolidBrush(System.Drawing.Color.Yellow)
Dim bg_colour As New System.Drawing.SolidBrush(System.Drawing.Color.LightGray)
' draw first appearance of dot on the screen
Public Sub prep(sender As Object, g As Graphics)
x_start = 10
y_start = sender.Height - 70
x_max = Math.Round(sender.Width / 2) - 5
y_max = 70
x = x_start
y = y_start
' constants
a = (y_start - y_max) / Math.Pow((x_start - x_max), 2)
b = -2 * a * x_max
c = y_max + a * Math.Pow(x_max, 2)
' clear entire used canvas area
g.FillRectangle(bg_colour, 0, 60, sender.Width, sender.Height)
' draw dot
g.FillEllipse(dot_colour, x, y, dotDIAMETER, dotDIAMETER)
End Sub
' repetitively clear and draw dot on the screen - Simulate motion
Public Sub play(sender As Object, g As Graphics)
' condition for continuing motion
Do While x < sender.Width - dotDIAMETER And y <= y_start
' redraw dot
g.FillEllipse(dot_colour, x, y, dotDIAMETER, dotDIAMETER)
x += 10
y = CInt(Math.Round(a * x * x + b * x + c))
' take a time pause
Threading.Thread.Sleep(50)
Loop
End Sub
End Class