Write an Equation of the Parabola Shown Calculator
Introduction & Importance
Deriving the equation of a parabola from its vertex and focus is a fundamental concept in mathematics. Our calculator simplifies this process, making it accessible to students and professionals alike.
How to Use This Calculator
- Enter the X and Y coordinates of the vertex and the height of the parabola.
- Click the “Calculate” button.
- View the derived equation and graph in the result section.
Formula & Methodology
The standard form of a parabola’s equation is y = a(x-h)2 + k, where (h, k) is the vertex. Given the vertex (x, y) and height (h), we can find ‘a’ using the formula a = 4p, where p is the distance from the vertex to the focus.
Real-World Examples
Data & Statistics
| Vertex (x, y) | Height (h) | Equation |
|---|---|---|
| (-2, 3) | 4 | y = 4(x + 2)2 + 3 |
| (1, -2) | 6 | y = 4(x – 1)2 – 2 |
Expert Tips
- Understand the direction of the parabola’s opening based on the height value.
- Verify the derived equation by plugging in the given vertex and height.
Interactive FAQ
What is the standard form of a parabola’s equation?
The standard form of a parabola’s equation is y = a(x-h)2 + k, where (h, k) is the vertex.
How do I find the focus of a parabola given its equation?
Given the equation y = a(x-h)2 + k, the focus is at (h, k + 1/(4a)).
For more information, see the Maths is Fun guide to parabolas.