Question 853902
Most but not all of what you want is discussed here:  


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


You should put the function into Standard Form.  Solving for x when f(x)=0 will then be a simple process, giving the x-axis intercepts.  Your function will have a minimum, because {{{a>0}}}.