elaborating on table saw techniques:
A pedant would insist that Brett's method gives a elipse,
rather than a parabola. A pragmatist will know that over the range of interest, the two are nearly indistinguishable.
Another way:
If you have a way to precisely control the fence and depth, you can make a stair step approximation of any curve, then sand the corners of the steps off. If you try to make the steps very fine you will find most blades do not cut a rectangular groove...the angles of the teeth leave an inverted vee.
One way to set the fence in equal increments is to clamp a block behind it, the add one more 1/8" shim for each cut. The height can be set with a machinist's height gauge or with a template.
For convex curves, If a thin amount of stock is left between the kerfs, it will support the block on the table for subsequent cuts, then broken out at the end.