Question 881498
Have Min?  YES because {{{3>0}}}.


Use Completing the Square to put the function into standard form and read the vertex (the minimum point) from the equation.  <a href="http://www.algebra.com/tutors/Completing-the-Square-to-Solve-General-Quadratic-Equation.lesson?content_action=show_dev">This shows how to Complete the Square.</a>


The function which you have is factorable enough that you can find the roots, and from the roots, find the x value at the vertex, and use this x value (exact mid point of the two roots) to compute the y value for the vertex.


{{{g(x)=3(x+1)(x+3)}}}, and finding roots:
{{{(x+1)(x+3)=0}}}
{{{x=-1}}}  or  {{{x=-3}}}.
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The exact middle of those x-intercepts is -2.  This is the line of symmetry of the function  and the minimum point of the parabola.
{{{g(-2)=3(-2+1)(-2+3)}}}
{{{3(-1)(1)}}}
{{{highlight(g(-2)=-3)}}}, the minimum value, vertex (-2,-3).