# Graphing Quadratic Functions

Graphically, a parabola represents a quadratic function f(x) = ax^{2} + bx + c. The method followed to graph a quadratic function makes use of the characteristics of the graph, like the vertex, axis of symmetry and intercepts etc. The sign of a, the leading coefficient determines whether the parabola opens up or down and whether the vertex is the lowest or the highest point in the graph of the quadratic equation. The graphical method is not always useful in finding the exact solution of quadratic equations. But, it can nevertheless be used in estimating the roots and also display clearly the maximum or minimum function value. The quadratic graphs are also useful in showing the regions representing quadratic inequalities.