I am programming a ball falling down from a cliff and bouncing back. The physics can be ignored and I want to use a simple $y = ax^2$ parabola to draw the falling ball.
I have given two points, the edge of the cliff at $C(-0.9; 0.8)$ and the point where the ball hits the bottom $B(0.1; -1.05)$. Due to its symmetry we know there is another point at $A(-1.9; -1.05)$. So that are 3 points I could work with. $C$ is the vertex.
I've tried this approach but my parabola is not as exact as I need it to estimate for example the intersects with the x- or y-axis.
As the legs of the parabola are down, all I can tell is that $a$ is negative:
$$ y = ax^2 + bx +c; a < 0 $$
I tried drawing it in Excel which allows to add an polynomial trendline. This is the best approximation I could do so far (dotted line).
But I need the function. Is it somehow possible to calculate the equation somehow?