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Initial commit: Quadratic Equation Plotter application

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Features:
- Plot quadratic equations: y = ax² + bx + c
- Adjustable X-axis range
- Visualize vertex and roots
- Save plots in multiple formats
- Interactive matplotlib navigation toolbar
- Clean GUI interface with Tkinter
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anas-rashid 2026-04-03 20:02:07 +02:00
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# Python
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# Quadratic Equation Plotter
A Python GUI application for plotting quadratic equations using Tkinter and Matplotlib.
## Features
- Plot any quadratic equation in the form: **y = ax² + bx + c**
- Adjustable X-axis range
- Visualize vertex and roots (when they exist)
- Save plots in multiple formats (PNG, JPEG, PDF, SVG)
- Interactive matplotlib navigation toolbar (zoom, pan, save)
- Clean, user-friendly interface
## Requirements
- Python 3.6 or higher
- NumPy
- Matplotlib
## Installation
1. Install Python dependencies:
```bash
pip install -r requirements.txt
```
Or install manually:
```bash
pip install numpy matplotlib
```
## Usage
Run the application:
```bash
python quadratic_plotter.py
```
### Interface Components:
1. **Coefficients Input**:
- Enter values for `a`, `b`, and `c`
- Default: a=1, b=0, c=0 (plots y = x²)
2. **X-axis Range**:
- Set the range of x-values to plot
- Default: -10 to 10
3. **Buttons**:
- **Plot Quadratic**: Generate the plot with current parameters
- **Save Plot**: Save the current plot to a file
- **Clear Plot**: Clear the current plot
4. **Plot Area**:
- Interactive matplotlib plot with zoom and pan capabilities
- Vertex shown as red dot (for a ≠ 0)
- Roots shown as green dots (when real roots exist)
- Legend showing equation and key points
## Example Plots
1. **Standard Parabola**: a=1, b=0, c=0
2. **Shifted Parabola**: a=1, b=-2, c=1
3. **Downward Parabola**: a=-1, b=0, c=4
4. **Linear Function**: a=0, b=2, c=1 (plots a straight line)
## Features in Detail
### Vertex Calculation
The vertex of the parabola is calculated using:
```
x_vertex = -b / (2a)
y_vertex = a(x_vertex)² + b(x_vertex) + c
```
### Roots Calculation
Real roots are calculated using the quadratic formula:
```
x = [-b ± √(b² - 4ac)] / (2a)
```
### Plot Customization
- Blue line: Quadratic curve
- Red dot: Vertex of parabola
- Green dots: Real roots (x-intercepts)
- Grid lines for easy reference
- Axes lines through origin
## Error Handling
The application includes error handling for:
- Invalid numeric input
- X-min greater than X-max
- File save errors
- Missing dependencies
## License
This project is open source and available for educational and personal use.
## Troubleshooting
If you encounter issues:
1. **Missing dependencies**: Ensure all packages are installed
2. **GUI not showing**: Check if Tkinter is installed (usually bundled with Python)
3. **Plot not updating**: Verify all input fields contain valid numbers
4. **ImportError: "NavigationToolbar2Tk" is not exported**: This application includes compatibility code for different matplotlib versions. If you see this error, update matplotlib to version 3.4 or later:
```bash
pip install --upgrade matplotlib
```
The code will automatically try multiple import locations for backward compatibility.
## Screenshot
![Quadratic Plotter Screenshot](screenshot.png)
*Note: Add your own screenshot after running the application*

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import tkinter as tk
from tkinter import ttk, messagebox
import numpy as np
from matplotlib.figure import Figure
from matplotlib.backends.backend_tkagg import FigureCanvasTkAgg
# Import NavigationToolbar2Tk with version compatibility
try:
# For matplotlib >= 3.4
from matplotlib.backends.backend_tkagg import NavigationToolbar2Tk # type: ignore
except ImportError:
try:
# For older matplotlib versions or alternative location
from matplotlib.backends._backend_tk import NavigationToolbar2Tk # type: ignore
except ImportError:
# Try another possible location
from matplotlib.backends.backend_tk import NavigationToolbar2Tk # type: ignore
class QuadraticPlotter:
def __init__(self):
self.root = tk.Tk()
self.root.title("Quadratic Equation Plotter")
self.root.geometry("900x700")
# Variables for coefficients
self.a_var = tk.StringVar(value="1")
self.b_var = tk.StringVar(value="0")
self.c_var = tk.StringVar(value="0")
# Variables for x-range
self.x_min_var = tk.StringVar(value="-10")
self.x_max_var = tk.StringVar(value="10")
# Create the main window content
self.create_widgets()
# Start the application loop
self.root.mainloop()
def create_widgets(self):
# Create main frames
control_frame = tk.Frame(self.root, padx=10, pady=10)
control_frame.pack(side=tk.TOP, fill=tk.X)
plot_frame = tk.Frame(self.root)
plot_frame.pack(side=tk.BOTTOM, fill=tk.BOTH, expand=True, padx=10, pady=10)
# Title
title_label = tk.Label(control_frame, text="Quadratic Equation Plotter: y = ax² + bx + c",
font=("Arial", 14, "bold"))
title_label.grid(row=0, column=0, columnspan=6, pady=(0, 15))
# Coefficients input
coeff_frame = tk.LabelFrame(control_frame, text="Coefficients", padx=10, pady=10)
coeff_frame.grid(row=1, column=0, columnspan=6, sticky="ew", pady=(0, 10))
# a coefficient
tk.Label(coeff_frame, text="a =").grid(row=0, column=0, padx=(0, 5))
a_entry = tk.Entry(coeff_frame, textvariable=self.a_var, width=10)
a_entry.grid(row=0, column=1, padx=(0, 15))
# b coefficient
tk.Label(coeff_frame, text="b =").grid(row=0, column=2, padx=(0, 5))
b_entry = tk.Entry(coeff_frame, textvariable=self.b_var, width=10)
b_entry.grid(row=0, column=3, padx=(0, 15))
# c coefficient
tk.Label(coeff_frame, text="c =").grid(row=0, column=4, padx=(0, 5))
c_entry = tk.Entry(coeff_frame, textvariable=self.c_var, width=10)
c_entry.grid(row=0, column=5, padx=(0, 15))
# X-range input
range_frame = tk.LabelFrame(control_frame, text="X-axis Range", padx=10, pady=10)
range_frame.grid(row=2, column=0, columnspan=6, sticky="ew", pady=(0, 10))
tk.Label(range_frame, text="From:").grid(row=0, column=0, padx=(0, 5))
xmin_entry = tk.Entry(range_frame, textvariable=self.x_min_var, width=10)
xmin_entry.grid(row=0, column=1, padx=(0, 15))
tk.Label(range_frame, text="To:").grid(row=0, column=2, padx=(0, 5))
xmax_entry = tk.Entry(range_frame, textvariable=self.x_max_var, width=10)
xmax_entry.grid(row=0, column=3, padx=(0, 15))
# Buttons
button_frame = tk.Frame(control_frame)
button_frame.grid(row=3, column=0, columnspan=6, pady=(10, 0))
plot_button = tk.Button(button_frame, text="Plot Quadratic", command=self.plot_quadratic,
bg="lightblue", font=("Arial", 10, "bold"), padx=20, pady=5)
plot_button.pack(side=tk.LEFT, padx=(0, 10))
save_button = tk.Button(button_frame, text="Save Plot", command=self.save_plot,
bg="lightgreen", font=("Arial", 10, "bold"), padx=20, pady=5)
save_button.pack(side=tk.LEFT, padx=(0, 10))
clear_button = tk.Button(button_frame, text="Clear Plot", command=self.clear_plot,
bg="lightcoral", font=("Arial", 10, "bold"), padx=20, pady=5)
clear_button.pack(side=tk.LEFT)
# Matplotlib figure and canvas
self.fig = Figure(figsize=(8, 6), dpi=100)
self.ax = self.fig.add_subplot(111)
self.setup_plot()
self.canvas = FigureCanvasTkAgg(self.fig, master=plot_frame)
self.canvas.get_tk_widget().pack(fill=tk.BOTH, expand=True)
# Add matplotlib navigation toolbar
self.toolbar = NavigationToolbar2Tk(self.canvas, plot_frame)
self.toolbar.update()
self.canvas.get_tk_widget().pack(fill=tk.BOTH, expand=True)
def setup_plot(self):
"""Initialize plot with labels and grid"""
self.ax.set_xlabel('x')
self.ax.set_ylabel('y')
self.ax.set_title('Quadratic Function: y = ax² + bx + c')
self.ax.grid(True, linestyle='--', alpha=0.7)
self.ax.axhline(y=0, color='k', linestyle='-', linewidth=0.5)
self.ax.axvline(x=0, color='k', linestyle='-', linewidth=0.5)
def plot_quadratic(self):
"""Plot the quadratic equation based on user input"""
try:
# Get coefficients
a = float(self.a_var.get())
b = float(self.b_var.get())
c = float(self.c_var.get())
# Get x-range
x_min = float(self.x_min_var.get())
x_max = float(self.x_max_var.get())
if x_min >= x_max:
messagebox.showerror("Input Error", "X-min must be less than X-max")
return
# Generate x values
x = np.linspace(x_min, x_max, 500)
y = a * x**2 + b * x + c
# Clear previous plot
self.ax.clear()
self.setup_plot()
# Determine equation type for title
if a != 0:
eq_type = "Quadratic Function"
elif b != 0:
eq_type = "Linear Function"
else:
eq_type = "Constant Function"
# Build equation string with only non-zero terms, formatted nicely
parts = []
if a != 0:
if a == 1:
parts.append("x²")
elif a == -1:
parts.append("-x²")
else:
parts.append(f"{a}x²")
if b != 0:
if b == 1:
parts.append("+ x" if parts else "x")
elif b == -1:
parts.append("- x" if parts else "-x")
else:
sign = "+" if b > 0 else "-"
parts.append(f"{sign} {abs(b)}x")
if c != 0:
sign = "+" if c > 0 else "-"
parts.append(f"{sign} {abs(c)}")
if not parts:
eq_str = "y = 0"
else:
# First term without leading plus
first = parts[0]
if first.startswith("+ "):
first = first[2:]
elif first.startswith("- "):
first = f"-{first[2:]}"
eq_str = "y = " + first + " " + " ".join(parts[1:])
self.ax.set_title(f"{eq_type}: {eq_str}")
# Plot the quadratic
self.ax.plot(x, y, 'b-', linewidth=2, label=eq_str)
# Calculate and plot vertex
if a != 0:
vertex_x = -b / (2 * a)
vertex_y = a * vertex_x**2 + b * vertex_x + c
self.ax.plot(vertex_x, vertex_y, 'ro', markersize=8, label=f'Vertex ({vertex_x:.2f}, {vertex_y:.2f})')
# Calculate and plot roots if they exist (real roots)
discriminant = b**2 - 4*a*c
# Handle quadratic case (a ≠ 0)
if a != 0:
if discriminant >= 0:
root1 = (-b + np.sqrt(discriminant)) / (2 * a)
root2 = (-b - np.sqrt(discriminant)) / (2 * a)
# For discriminant == 0, both roots are the same
if abs(root1 - root2) < 1e-10: # Essentially equal
self.ax.plot(root1, 0, 'go', markersize=8, label=f'Double Root ({root1:.2f}, 0)')
else:
self.ax.plot(root1, 0, 'go', markersize=8, label=f'Root1 ({root1:.2f}, 0)')
self.ax.plot(root2, 0, 'go', markersize=8, label=f'Root2 ({root2:.2f}, 0)')
else:
# Complex roots - show message in legend
self.ax.text(0.02, 0.02, 'Complex Roots', transform=self.ax.transAxes,
fontsize=10, color='red', bbox=dict(boxstyle='round', facecolor='yellow', alpha=0.5))
# Handle linear case (a = 0, b ≠ 0)
elif b != 0:
root = -c / b
self.ax.plot(root, 0, 'go', markersize=8, label=f'Root ({root:.2f}, 0)')
# Handle constant case (a = 0, b = 0)
else:
if c == 0:
self.ax.text(0.02, 0.02, 'Infinite Roots (y = 0)', transform=self.ax.transAxes,
fontsize=10, color='blue', bbox=dict(boxstyle='round', facecolor='lightblue', alpha=0.5))
else:
self.ax.text(0.02, 0.02, 'No Roots (horizontal line)', transform=self.ax.transAxes,
fontsize=10, color='red', bbox=dict(boxstyle='round', facecolor='lightcoral', alpha=0.5))
# Add legend
self.ax.legend(loc='best')
# Refresh canvas
self.canvas.draw()
except ValueError:
messagebox.showerror("Input Error", "Please enter valid numbers for all coefficients and range")
def clear_plot(self):
"""Clear the plot"""
self.ax.clear()
self.setup_plot()
self.canvas.draw()
def save_plot(self):
"""Save the current plot to a file"""
try:
from tkinter import filedialog
import os
filetypes = [
('PNG files', '*.png'),
('JPEG files', '*.jpg'),
('PDF files', '*.pdf'),
('SVG files', '*.svg'),
('All files', '*.*')
]
filename = filedialog.asksaveasfilename(
defaultextension=".png",
filetypes=filetypes,
title="Save Plot As"
)
if filename:
self.fig.savefig(filename, dpi=300, bbox_inches='tight')
messagebox.showinfo("Success", f"Plot saved successfully as:\n{os.path.basename(filename)}")
except Exception as e:
messagebox.showerror("Save Error", f"Could not save plot: {str(e)}")
if __name__ == "__main__":
app = QuadraticPlotter()

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numpy>=1.21.0
matplotlib>=3.5.0