In general, a parabola is formed when you graph a quadratic function. A quadratic is in the form: where a,b and c are constants.
The parabola shape really comes from the x2 term, which you can see above, which is the graph of y = x2. This is the absolute simplest quadratic where b=0, c=0 and a=1.
Regardless of the values of a b and c, the graph is a parabola. Their values alter it's shape and position in various ways. This is explored in depth in Quadratic Explorer, where you modify a,b and c with sliders to observe the effect on the parabola's shape.