Question 904278
The explanation you want is in this lesson:


<a href="http://www.algebra.com/my/Completing-the-Square-to-Solve-General-Quadratic-Equation.lesson?content_action=show_dev">http://www.algebra.com/my/Completing-the-Square-to-Solve-General-Quadratic-Equation.lesson?content_action=show_dev</a>


That will help you for the standard form, as much as for finding the vertices and the zeros.


{{{graph(300,300,-6,6,-6,6,3x^2-6x+1,-x^2-3x+3)}}}