The equation given is:

$y = (x + 2)^2 + 5$

This is a transformed version of the parent function $y = x^2$, which is a standard parabola opening upwards. Here’s how each part of the equation affects the graph:

1. Horizontal Shift: The $(x + 2)$ inside the square indicates a horizontal shift. Since it’s $(x + 2)$, the graph shifts 2 units to the left.
2. Vertical Shift: The $+ 5$ outside the square moves the graph 5 units up.

As a result, the vertex of the parabola, which is normally at $(0, 0)$ for $y = x^2$, is now at $(-2, 5)$.

The transformed graph should show a parabola opening upwards with its vertex at $(-2, 5)$.

Would you like a further breakdown of these transformations or have any specific questions?

Here are some related questions:

1. What is the effect of a negative sign in front of the squared term, such as in $y = -(x+2)^2 + 5$?
2. How would the graph change if we had $(x - 2)^2 + 5$ instead?
3. What happens if we add a coefficient to the squared term, like $y = 2(x+2)^2 + 5$?
4. How does the vertex form of a parabola help in quickly identifying transformations?
5. Can we rewrite $y = (x + 2)^2 + 5$ in standard form?

Tip: When graphing transformations, start with the vertex shift and then apply other transformations like stretching or reflecting.