A quadratic equation is represented graphically as:

Here the graph represents the parabola where (h,k) is the vertex of the parabola.
Put any value of h, k and a to get the graph as follows:
The graph of a quadratic equation is parabolic in nature.
Suppose that you have a quadratic equation given by:

Convert the equation into perfect square by completing the square method

This is the method of conversion of quadratic to plot the graph.