Find Equation Given Zeros and Y-Intercept Calculator
Introduction & Importance
Finding an equation given zeros and a y-intercept is a fundamental concept in algebra. It’s crucial for understanding the behavior of a function and its relationship with the x and y axes.
How to Use This Calculator
- Enter the two zeros and the y-intercept of the function.
- Click “Calculate”.
- View the calculated equation and chart below.
Formula & Methodology
The general form of a quadratic equation is ax² + bx + c. Given two zeros (roots), r1 and r2, and a y-intercept c, the equation can be found using the formula:
a = (r1 - r2)², b = -2 * (r1 + r2), c = r1 * r2
Real-World Examples
Data & Statistics
| Equation | Roots | Y-Intercept |
|---|---|---|
| x² – 5x + 6 | 2, 3 | 6 |
| x² – 4x + 3 | 1, 3 | 3 |
Expert Tips
- Always double-check your inputs for accuracy.
- Remember, the y-intercept is the point where the graph crosses the y-axis.
Interactive FAQ
What are the roots of a quadratic equation?
The roots of a quadratic equation are the values of x that make the equation equal to zero.