Write Quadratic Equation Given X-Intercepts and Point Calculator
Introduction & Importance
Writing a quadratic equation using x-intercepts and a point is a fundamental concept in algebra. This calculator simplifies the process, making it accessible to everyone.
How to Use This Calculator
- Enter the x-intercepts (x1 and x2) and the y-coordinate of the point.
- Click ‘Calculate’.
- View the generated quadratic equation and chart.
Formula & Methodology
The quadratic equation is formed using the formula: y = ax² + bx + c, where a, b, and c are coefficients. The x-intercepts and the point are used to solve for these coefficients.
Real-World Examples
Data & Statistics
| Equation | X-intercepts | Vertex |
|---|---|---|
| y = 2x² – 5x + 3 | (-1, 0), (3, 0) | (-1, 4) |
| y = -x² + 6x – 8 | (2, 0), (4, 0) | (3, -1) |
| Equation | Domain | Range |
|---|---|---|
| y = 2x² – 5x + 3 | All real numbers | [-∞, +∞) |
| y = -x² + 6x – 8 | All real numbers | [-∞, +∞) |
Expert Tips
- Always check your answers by substituting the x-intercepts and the point into the generated equation.
- For more complex equations, consider using a graphing calculator or software.
Interactive FAQ
What are x-intercepts?
X-intercepts are the points where a quadratic function crosses the x-axis. They can be found by setting y = 0 and solving for x.
How do I find the vertex of a quadratic equation?
The vertex of a quadratic equation can be found using the formula: x = -b / 2a. The y-coordinate of the vertex is then found by substituting this value of x back into the equation.