The problem is asking to graph the function $h(x) = (x + 5)^2 + 4$ using transformations of $f(x) = x^2$.

Analyzing the function $h(x) = (x + 5)^2 + 4$:

1. The base function is $f(x) = x^2$, which is a standard parabola with its vertex at the origin (0,0).
2. The transformation $(x + 5)^2$ implies a horizontal shift to the left by 5 units.
3. The transformation $+4$ at the end represents a vertical shift up by 4 units.

Therefore, the function $h(x) = (x + 5)^2 + 4$ is the graph of $f(x) = x^2$, shifted 5 units to the left and 4 units upward. This matches option A: "The graph of $f(x) = x^2$ should be horizontally shifted to the left by 5 units and vertically shifted up by 4 units."

Would you like more details on graph transformations, or do you have any questions?

Related Questions:

1. What is a horizontal shift in a graph?
2. How do vertical shifts affect the graph of a function?
3. Can transformations apply to other types of functions, like cubic or absolute value functions?
4. What is the vertex of a parabola, and how do shifts affect it?
5. How would you describe the transformation of $f(x) = x^2$ into $h(x) = (x - 3)^2 - 2$?

Tip: Horizontal shifts are always in the opposite direction of the sign inside the function. For example, $(x + 5)$ means a shift to the left, not the right!