Can somebody teach what quadratic function is?

A quadratic function is one of the form f(X)=ax^2+bx +c,where a,b and c are numbers with 'a' not equal to zero.
The graph of a quadratic function is a curve called a parabola. Parabola may open upward or downward and vary in 'width' or 'steepness' , but all have the basic "U" shape.
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 the 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.

Hope this was helpful...!!!