How it Works
Uses the Quadratic Formula: x = [-b ± √(b² - 4ac)] / 2a.
What is Quadratic Trajectory Solver?
Solves ax² + bx + c = 0 to find where a projectile hits the ground or a curve intersects zero.
Step-by-Step Guide
- 1 Input A
- Gravity/Curve coefficient (non-zero).
- 2 Input B
- Slope/Velocity.
- 3 Input C
- Starting Height/Intercept.
- 4 Solve
- Find the roots (intercepts).
Example
Input: 1x² - 5x + 6 = 0
Result: x = 3, x = 2
FAQ
What is the Discriminant?
The part under the square root (b² - 4ac). It tells you how many solutions exist.
What if the result is negative?
In physics (time), you usually discard the negative root. In math, it's valid.
What are imaginary roots?
If the discriminant is negative, the curve never touches the x-axis (no real solution).
Real world use?
Calculating the arc of a basketball shot or satellite dish shape.
Can A be zero?
No, then it becomes a linear equation, not quadratic.
Conclusion
Essential for physics students calculating hang time or business analysts finding break-even points on curved profit models.