What is Terminology of Quadratic Functions ?

The function in x given by: F(x) = ax² + bx + c, where a 0 is called a quadratic function. The graph of a quadratic function is called a parabola. Each point on a parabola is a reflection of another point on the parabola with respect to a line of symmetry called the axis of the parabola. The point where the axis of symmetry traverses through the parabola is called the vertex. The vertex point can be thought of as the "minimum" or "maximum" point on the graph. The leading coefficient of the function, in other words the "a" part, dominates what happens in the graph of the parabola. As x gets very large in a positive or negative direction, the graph either opens upward, or opens downward. These two situations are illustrated below:

Notice that in this last example, that as the lead coefficient becomes larger in a positive way, or smaller in a negative way, that the graph of the parabola becomes "narrower".