Write a Quadratic Function with Given Zeros Calculator
Introduction & Importance
Writing a quadratic function with given zeros is a fundamental concept in algebra. It’s crucial for understanding and solving quadratic equations, which have numerous applications in physics, engineering, and data analysis.
How to Use This Calculator
- Enter the two zeros of the quadratic function.
- Click the “Calculate” button.
- View the resulting quadratic function and graph.
Formula & Methodology
The formula for a quadratic function with given zeros (a, b) is:
f(x) = a(x – zero1)(x – zero2)
Real-World Examples
Example 1
Given zeros: -2, 3
f(x) = 5(x + 2)(x – 3)
Example 2
Given zeros: 0, 4
f(x) = -3x(x – 4)
Data & Statistics
| Zeros | Function | Vertex |
|---|---|---|
| -2, 3 | 5(x + 2)(x – 3) | (-0.5, -10) |
| 0, 4 | -3x(x – 4) | (2, 0) |
Expert Tips
- To find the vertex of a quadratic function, use the formula vertex = (-b/2a, f(-b/2a)).
- Remember that the leading coefficient ‘a’ determines the direction of the parabola.
Interactive FAQ
What if my zeros are the same?
If your zeros are the same, you have a repeated root, and the function becomes a simple linear function: f(x) = a(x – zero).
Can I use this calculator for complex zeros?
No, this calculator only works with real zeros. For complex zeros, you would need a different tool.