Question 1066249
f(x)=3x^2+6x+2
function opens upward because positive coefficient in front of x^2.  It decreases from x=-oo to x=-1 and increases from x >-1.
domain is all x. 
vertex x-value is -b/2a or -6/3(2)=-1
f(-1)=3-6+2=-1. 
Vertex is (-1,-1)
axis of symmetry is x=-1
Range is [-1,oo)
y intercept is at f(0), and that = 2
x-intercepts need quadratic formula
x=(1/6)(-6 +/- sqrt (36-24))= (1/6)(-6 +/- 2 sqrt (3))= -1 +/- ((1/3) sqrt (3)).  Numerically, they are -.42 and -1.58

{{{graph(300,300,-5,3,-10,10,3x^2+6x+2)}}}