Modeling Projectile Motion with Parabolas

You can perfectly model throwing an object over a wall starting with just y = -x².

Seriously. Let's say the wall is 9 meters high. First, you shift the curve

up by 9, so the equation becomes y = -x² + 9. Now the peak is

at 9 meters, but the path is too narrow. To make the object travel farther,

you stretch the curve horizontally. Then, to make the throw start at your feet,

at the (0,0) origin point, you just slide the whole graph sideways. And just like that,

you have the exact mathematical formula for that perfect arc.