Question: For example in Peggle or Apple Jack, the user can move around a curve showing where the ball (or the washing machine / panda or whatever) is about to go before the user has requested that the projectile is launched. I know i need to use an equation to plot the points but I'm no mathematician (anymore :(). Can anybody be so kind as to provide me with the correct equation and tell me what I should substitute in to get my X any Y values given a certain time and initial velocity.

Answer: 
Take a look at my answer to [this question](https://stackoverflow.com/questions/3273396/animate-sprite-along-a-curve-path-in-xna/3275116#3275116).

Taken from that answer, the formula you should be using is:

```
s = s₀ + v₀t + ½at²

```

*(Displacement equals: initial displacement, plus initial velocity multiplied by time, plus half acceleration multiplied by time squared.)*

Everything except time there is a vector (acceleration will be your downwards gravity). So simply use that equation on both your X and your Y axis.

Of course - the only way to guarantee that the plotted path will match your prediction equation *exactly* is if they are the same. That is the only way I can see for you to add support for predicting bounces.

If your actual game uses something different (like a full physics simulator), and you don't need to predict bounces, and you don't have to be perfectly accurate - then this will give you a suitable approximation for the prediction.
You could use newton's method of approx. solving. The problem here is that you need to integrate - so you have to define the trade-off between preciseness and calculation time. 

**RK4** is the method that is best in my opinion - it is fast and still very precise.

You can read more info at <http://gafferongames.com/game-physics/integration-basics/>