The graph of a quadratic function is a curve called a parabola . The picture below shows three graphs, and they are all parabolas.
All parabolas are symmetric with respect to a line called the axis of symmetry .
A parabola intersects its axis of symmetry at a point called the vertex of the parabola. You know that two points determine a line. This means that if you are given any two points in the plane, then there is one and only one line that contains both points. A similar statement can be made about points and quadratic functions. Given three points in the plane that have different first coordinates and do not lie on a line, there is exactly one quadratic function f whose graph contains all three points.