Consider a graph with the y-axis as vertical, and the x-axis as horizontal. Treat f(x) as y. You graph y=x2-1
It's the standard parabola, opening upwards, with vertex at the origin,(0,0), but shifted down by one unit, so the vertex is (0,-1).
If you have y=x2-4, it shifts the parabola down by 4 units, so the vertex, the minimum point, is (0,-4)
It shifts the x2-1 parabola down by 3 units to x2-4. Every point on the graph is shifted downward by 3 units from the original graph.
Or shifted down by 4 units from the parabola y=x2
Alternatively, you could think of keeping the parabola in exactly the same position, and shift the x-axis upwards by 3 units