The Ballistic Flight Parabolic Equation calculator computes the parabolic equation coefficients based on the launch angle above the horizon (θ) at an initial velocity (V) assuming a constant downward acceleration (g).
INSTRUCTIONS: Choose units and enter the following:
Parabolic Flight Equation: The calculator returns the equation of the parabola to match the flight. It also returns the maximum ballistic range and max height achieved.
y = a•x² + b•x + c
The addition of the initial height (h) to the Max Altitude and Range have the effect of shifting the parabola to the right, when all that is wanted is a shift up.
One of the most common representations of a parabola in nature is an object moving in the gravitational field of a massive body, such as the projectile motion of a body affected by the Earth's gravity. The figure shows the parabolic trajectory typifying a projectile that is affected solely by gravity, g.
[Figure] Initial velocity of parabolic throwing
Source: Wikipedia / Fizped (modified to include motion equation)