This is some idea I improved upon a discussion between me and DJ Omnimaga today, might be pretty interesting.

So this game should kinda look like Angry Birds or clay shooting or something, but the shoot should be input as 3 values, a, b and c, then the projectile should be shot against a y=ax+bx+c curve. Of course, there would be restrictions:

- a<0 (you don't want to shoot the ground or divide by 0)
- The shooting range is at (0,0), so the player should make sure one of the zeroes of the function is x=0 and the other one is positive.
- b-4ac>=0 or else the quadratic function to check the above would error.

And obviously there would be a goal or else its not a game. How about shooting at a (x,y) coordinate? Maybe at 2 (x,y) coordinates at the same time? (Another, more complicated idea would be to make the player shoot in a pyramid of objects that could fall like in the actual Angry Birds game, but I might go for the simpler idea.)

So, in conclusion, this might be pretty challenging and also educational while the player learns about polynomial functions.
Nice! If you look up the equations for parabolic motion, it's y = .5*a*t^2 + v0y*t + y0. You need a second equation, x = x0 + v0x*t, to solve for t (t = (x-x0)/v0x) to get an equation for v0 purely in terms of x and y. Definitely a great idea, though, and you can always make it just be about the quadratic equation, then link that to the equations for parabolic motion at the end. Good luck! What language will you be using? TI-BASIC?
Most likely, yeah, TI-BASIC. I'll check this out when I'll get time.
  
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