Finding the next point on a Bezier Curve with Vector3's

I'm creating a bouncing game where the objective is to catch a falling ball going from one point to another, I'm not using physics for the bouncing effect, instead of I'm using a bezier curve to simulate the angle.

The way it's getting calculated is I'm using four Vector3's. p0 through p3

p0 will be the balls current transform.position, easy enough (example: -2.5, 0, 0). p2 will be the intercept point, it is at this point where you're able to catch the ball, we know that as well. (2.5, 0, 0) p1 we can figure out because we're specifying a y, value, and the x value you will be the position between p0 and p2. ((2.5 + -2.5)/2, 2.5, 0) or (0, 2.5, 0)

But where I'm getting hung up is what the value of p3 should be. Again, we're setting a static y value, no issue there. But I can't figure out how to get x. I know that in this example it's going to be 5, because that's the next logical step, but I don't know the math to get 5. The point of this step is just to have the ball keep falling past the play area naturally

The ball's x position can be other values besides 2.5, sometimes the ball will bounce in place. (So p2 would also be (-2.5, 0, 0)) and I think that's throwing a wedge into the math I'm trying to figure out.

I've attached an image of what I'm trying to accomplish.