y=x^2+4x+4=(x+2)^2.
a) Vertex is when y is minimum or maximum. The quantity (x+2)^2 is always ≥0 so its minimum value is 0 when x=-2. That makes the vertex (-2,0).
b) The vertex is always on the axis of symmetry, which in this case is the line, x=-2. The axis of symmetry is like a mirror reflecting the left and right halves of the parabola.
c) Intercepts. When x=0 we have the y intercept y=4; when y=0 we have the x intercept, x=-2. At x=-2 the graph touches the x-axis without cutting or intercepting it.
d) Graph:
