The problem asks to choose the graph of $g(x) = (x + 5)^2$ and compare it to its parent function $f(x) = x^2$. Then, you're asked to describe the transformation.

Step-by-step explanation:

1. Parent Function: The parent function $f(x) = x^2$ is a standard parabola with its vertex at $(0, 0)$.

2. Transformation in $g(x) = (x + 5)^2$:

   • The equation $g(x) = (x + 5)^2$ represents a horizontal translation of the parent function $f(x) = x^2$.
   • The transformation $x + 5$ means the graph shifts 5 units to the left.

3. Identifying the graph:

   • We look for the graph that has the same shape as $f(x) = x^2$ but shifted 5 units left.
   • Based on the images, Graph C shows the correct transformation, where the parabola is shifted to the left.

4. Correct Description:

   • The horizontal translation of 5 units to the left is described by option G.

Final Answer:

• Graph C and Option G describe the transformation of the function.

Would you like more details on transformations or any other specific questions?

Here are some related questions to expand your understanding:

1. What is a vertical translation, and how does it affect the function?
2. How would the graph change if the equation were $g(x) = (x - 5)^2$?
3. What does a horizontal stretch or compression look like for a parabola?
4. How do vertical and horizontal translations affect the vertex of a quadratic function?
5. What if the function was $g(x) = x^2 + 5$ instead of $(x + 5)^2$?

Tip: Always look inside the parentheses for horizontal transformations and outside for vertical ones!