R Parabola Plotter

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name: r-parabola-plotter description: Create parabola plots using R with customizable coefficients, range, styling, and annotations. Use for mathematical visualization, quadratic function analysis, and educational demonstrations of parabolic curves.

Overview

This skill generates professional parabola plots using R's ggplot2 library. It handles quadratic functions of the form y = ax² + bx + c with full customization options including vertex marking, axis of symmetry, and roots.

When to Use This Skill

Use this skill when the user asks to:

• Plot a parabola or quadratic function
• Visualize y = ax² + bx + c
• Graph polynomial functions (degree 2)
• Show quadratic relationships
• Create mathematical visualizations with parabolas
• Demonstrate vertex, roots, or axis of symmetry

Required Information

To create a parabola plot, you need:

• Coefficient a (default: 1) - Controls width and direction
• Coefficient b (default: 0) - Controls horizontal position
• Coefficient c (default: 0) - Controls vertical position
• X range (default: -10 to 10) - Domain to plot

R Code Template

Always use this template structure:

# Install and load required packages
if (!require("ggplot2")) install.packages("ggplot2")
library(ggplot2)

# Define parabola coefficients
a <- 1    # Change this value
b <- 0    # Change this value
c <- 0    # Change this value

# Define x range
x_min <- -10
x_max <- 10

# Create data
x <- seq(x_min, x_max, length.out = 500)
y <- a * x^2 + b * x + c

# Create data frame
df <- data.frame(x = x, y = y)

# Calculate vertex
vertex_x <- -b / (2 * a)
vertex_y <- a * vertex_x^2 + b * vertex_x + c

# Calculate roots (if they exist)
discriminant <- b^2 - 4*a*c
has_real_roots <- discriminant >= 0

if (has_real_roots) {
  root1 <- (-b + sqrt(discriminant)) / (2*a)
  root2 <- (-b - sqrt(discriminant)) / (2*a)
}

# Create the plot
p <- ggplot(df, aes(x = x, y = y)) +
  geom_line(color = "blue", size = 1.2) +
  geom_hline(yintercept = 0, linetype = "dashed", color = "gray50") +
  geom_vline(xintercept = 0, linetype = "dashed", color = "gray50") +
  geom_point(aes(x = vertex_x, y = vertex_y), 
             color = "red", size = 3, shape = 19) +
  geom_vline(xintercept = vertex_x, linetype = "dotted", 
             color = "red", alpha = 0.5) +
  annotate("text", x = vertex_x, y = vertex_y, 
           label = sprintf("Vertex (%.2f, %.2f)", vertex_x, vertex_y),
           hjust = -0.1, vjust = 1.5, color = "red", size = 4) +
  labs(
    title = sprintf("Parabola: y = %.2fx² + %.2fx + %.2f", a, b, c),
    subtitle = sprintf("Vertex: (%.2f, %.2f)", vertex_x, vertex_y),
    x = "x", 
    y = "y"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    plot.title = element_text(face = "bold", hjust = 0.5),
    plot.subtitle = element_text(hjust = 0.5),
    panel.grid.minor = element_blank()
  )

# Add roots if they exist
if (has_real_roots) {
  p <- p + 
    geom_point(aes(x = root1, y = 0), 
               color = "green", size = 3, shape = 17) +
    geom_point(aes(x = root2, y = 0), 
               color = "green", size = 3, shape = 17) +
    annotate("text", x = root1, y = 0, 
             label = sprintf("Root (%.2f, 0)", root1),
             hjust = 0.5, vjust = -1, color = "green", size = 3.5) +
    annotate("text", x = root2, y = 0, 
             label = sprintf("Root (%.2f, 0)", root2),
             hjust = 0.5, vjust = -1, color = "green", size = 3.5)
  
  p <- p + labs(
    subtitle = sprintf("Vertex: (%.2f, %.2f) | Roots: %.2f, %.2f", 
                      vertex_x, vertex_y, root1, root2)
  )
} else {
  p <- p + labs(
    subtitle = sprintf("Vertex: (%.2f, %.2f) | No real roots", 
                      vertex_x, vertex_y)
  )
}

# Display the plot
print(p)

# Save the plot
ggsave("parabola_plot.png", plot = p, width = 10, height = 7, dpi = 300)
cat("\nPlot saved as 'parabola_plot.png'\n")

Customization Options

Basic Parabolas

• Standard parabola: a=1, b=0, c=0 → y = x²
• Inverted parabola: a=-1, b=0, c=0 → y = -x²
• Wider parabola: a=0.5, b=0, c=0 → y = 0.5x²
• Narrower parabola: a=2, b=0, c=0 → y = 2x²

Shifted Parabolas

• Vertical shift: Keep a=1, b=0, change c
• Horizontal shift: Keep a=1, c=0, change b
• Both shifts: Modify b and c together

X Range Adjustment

# For wide parabolas, use larger range
x_min <- -20
x_max <- 20

# For narrow parabolas, use smaller range
x_min <- -5
x_max <- 5

# Asymmetric ranges are fine too
x_min <- -15
x_max <- 5

Color Schemes

# Change the main curve color
geom_line(color = "darkblue", size = 1.5)

# Change vertex color
geom_point(..., color = "darkred", size = 4)

# Change roots color
geom_point(..., color = "darkgreen", size = 4)

Instructions for Response

When creating a parabola plot:

1. Ask for coefficients if not provided:

   • "What values would you like for a, b, and c?"
   • Or suggest defaults: "I'll use a=1, b=0, c=0 for a standard parabola"

2. Modify the template:

   • Replace the a, b, c values
   • Adjust x_min and x_max if needed
   • Keep all the vertex and root calculations

3. Provide the complete R code:

   • Include all necessary libraries
   • Use the full template (don't abbreviate)
   • Ensure code is ready to run as-is

4. Explain the plot features:

   • Where the vertex is located
   • Whether roots exist and where
   • The direction (opens up/down)
   • Any special characteristics

5. Suggest variations:

   • "Want to see it with different coefficients?"
   • "Would you like to compare multiple parabolas?"
   • "Should I adjust the x-range to show more detail?"

Example Responses

Example 1: Simple Request

User: "Plot a parabola"

Response: "I'll create a standard parabola plot (y = x²) for you using R. Here's the code:"

[Include full code with a=1, b=0, c=0]

"This creates a parabola that:

• Opens upward (a > 0)
• Has its vertex at the origin (0, 0)
• Is symmetric about the y-axis
• Passes through the origin (which is both the vertex and a root)"

Example 2: Specific Function

User: "Plot y = 2x² - 4x + 1"

Response: "I'll plot the parabola y = 2x² - 4x + 1. Here's the R code:"

[Include full code with a=2, b=-4, c=1]

"This parabola:

• Opens upward (a = 2 > 0)
• Has vertex at (1, -1)
• Has axis of symmetry at x = 1
• Has two real roots at approximately x = 0.29 and x = 1.71"

Example 3: Educational Context

User: "Show me how changing 'a' affects the parabola"

Response: "Great question! Let me create code that plots multiple parabolas with different 'a' values to demonstrate the effect:"

[Provide code that overlays multiple parabolas]

Common Variations

Multiple Parabolas on One Plot

# Create data for multiple parabolas
df_multi <- data.frame()
a_values <- c(0.5, 1, 2, -1)

for (a in a_values) {
  x <- seq(-5, 5, length.out = 200)
  y <- a * x^2
  temp_df <- data.frame(x = x, y = y, 
                        a = as.factor(sprintf("a = %.1f", a)))
  df_multi <- rbind(df_multi, temp_df)
}

ggplot(df_multi, aes(x = x, y = y, color = a)) +
  geom_line(size = 1.2) +
  theme_minimal() +
  labs(title = "Effect of coefficient 'a' on parabola shape",
       color = "Coefficient")

Interactive Plot (using plotly)

library(plotly)

plot_ly(df, x = ~x, y = ~y, type = 'scatter', mode = 'lines',
        name = sprintf('y = %.2fx² + %.2fx + %.2f', a, b, c)) %>%
  layout(title = "Interactive Parabola Plot",
         xaxis = list(title = "x", zeroline = TRUE),
         yaxis = list(title = "y", zeroline = TRUE))

Error Handling

If the user provides invalid input:

• Non-numeric coefficients: Ask for numbers
• a = 0: Explain this isn't a parabola (it's linear)
• Extreme values: Suggest adjusting x-range or y-range

Quality Checklist

Before providing the final code, ensure:

• Coefficients a, b, c are clearly defined
• X range is appropriate for the parabola width
• Vertex calculation is included
• Root calculation handles the discriminant
• Plot includes proper labels and title
• Vertex is marked and labeled
• Roots are marked if they exist
• Code is complete and runnable
• Plot will be saved to a file