The U shape is called a parabola
If the "a" is positive, then the parabola opens upward as shown in the graph on the left.
If "a" is negative, then the parabola opens downward. This is the parabola on the right.
The way I remember is that "a" being positive means it puts a smile on, which is what the parabola on the left resembles. The parabola on the right is a frowny face so "a" is negative.
A parabola is vertically cut in half by the axis of symmetry. One half mirrors over this vertical line to get the other half. The axis of symmetry passes through the vertex. The vertex is either the highest point or the lowest point depending on whether 'a' is negative or positive.