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: 
Simulation would probably be the **easiest** route to go down: create a dummy object with the specified properties and create a loop to apply the forces and say output the positions to an array and then display it, say: draw a line between the positions or draw a "ghost" of the projectile at each position.

A positive thing about simulation is you can control the balance of speed and accuracy by changing how often you record the positions.
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/>