Parabola Properties Calculator

Unlock the secrets of parabolas! Calculate vertex, focus, and visualize the curve with ease.

Parabola Equation

Select the orientation of the parabola and input the parameters \(h\), \(k\), and \(p\).

Enter Parameters

Properties

Vertex (V): $$V(x, y) = (h, k)$$
X:
Y:
Focus (F): $$F(x, y) = (h, k+p)$$ (Vertical) or $$F(x, y) = (h+p, k)$$ (Horizontal)
X:
Y:

Parabola Visualization

Understanding Parabola Properties

A parabola is a symmetrical U-shaped curve. Key properties include the vertex, the point where the parabola changes direction, and the focus, a point that helps define the shape of the parabola.

Formulas & Definitions

  • Vertical Parabola: Equation is given by \((x-h)^2 = 4p(y-k)\).
    • Vertex (V): \((h, k)\)
    • Focus (F): \((h, k+p)\)
  • Horizontal Parabola: Equation is given by \((y-k)^2 = 4p(x-h)\).
    • Vertex (V): \((h, k)\)
    • Focus (F): \((h+p, k)\)
  • \(h\), \(k\) define the vertex position, and \(p\) determines the shape and direction of the parabola.

How to Use This Calculator

1. Select Orientation: Choose between vertical or horizontal parabola. 2. Enter Parameters: Input the values for \(h\), \(k\), and \(p\). These values define the parabola's position and shape. 3. Calculate: Press the "Calculate" button to find the vertex and focus. 4. View Results: The vertex and focus coordinates will be displayed, and a visualization of the parabola will be shown below. 5. Copy Output: Use the copy icons to easily copy the calculated coordinates.