Aparabola is given by the equation y = x^2 + 4x + 4.
the vertex of the parabola is
. the focus of the parabola is
. the directrix of the parabola is given by the equation y =
.

Y = x² + 4x + 4.. Since the coefficient of x² =1, is positive, then this parabola opens upward & has a minimum.

Its axis of symmetry is = -b/a = -4/1 = 4 (so x=4)

1) When x=4, y= 4²+4(4)+4 => y=36 so the VERTEX has a minimum is at (4,36) 

2)FOCUS.: To be able to calculate the focus, rewrite the equation in a standard form: y-k =a(x-h)² & y = x² + 4x + 4 could be written y=(x+2)², this means that k=0 & h=-2.
Now p being the distance between the VERTEX & the FOCUS, we apply the formula (x-2)² = 4P (y-k) , but k=0 & h=2 then (x-2)² = 4P(y-0) then P =1/4

3) DRECTRICE : y=k-P = 0-1/4 ==> y=-1/4 is the directrix