The graph of g is obtained by translating the graph of f to the left 4 units and down 2 units.
Practice makes perfect
Let's start by pointing out the vertices of the given parabolas.
f
g
Vertex
(0,0)
(-4,-2)
Additionally, we can see that starting from the vertex of f that if we move one unit to the right then the y-coordinate moves one unit up. The graph of g holds the same property.
This implies that to obtain g starting from f we do not have to make either a vertical or horizontal stretch/shrink. This tells us that instead we just need to make both a vertical and a horizontal translation. The coordinates of the vertex of g give us a clue of the translations we need to make. The vertex is ( -4, -2), meaning that we have to translate the vertex of f to the left 4 units and 2 units down.
In conclusion, the graph of g is obtained by translating the graph of f to the left 4 units and 2 units down. This can be written algebraically as g(x)=f(x+4)-2.
