As I understand it, a parabola is the shape that results when you plot a quadratic equation in the XY plane

y = ax**2 + bx + c

In other words, it is any expression that has an x "squared" in it. The shape is like a cup (or inverted cup) with a single minimum (or maximum) value at the center.

A sinusoidal function is different in that it is periodic (repeating) and the slope of the curve is completely different. It has an infinite number of minima and maxima (because it repeats)