Question 636516
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Hi,
Note: the vertex form of a Parabola opening up(a>0) or down(a<0), {{{y=a(x-h)^2 +k}}} 
where(h,k) is the vertex  and  x = h  is the Line of Symmetry
1. f(x)= x^2+ 4  | parabola opeing UPward, V(0,4), doesNOT cross x-axis
2. {{{g(x)= x^2+ x+ 12= (x+1/2)^2 + 11&3/4}}}, parabola opeing UPward, V(-1/2,11.75), doesNOT cross x-axis 
{{{drawing(300,300,   -6, 6, -6, 20,  blue(line(-.5,20,-.5,-6))  , grid(1),
circle(0, 4,0.3),
circle(-.5, 11.75,0.3),
graph( 300, 300, -6, 6, -6, 20,0,x^2+ 4,x^2+ x+ 12 ))}}}