The equation provided in the image is:

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

Let's solve for $y$ in terms of $x$.

Step-by-Step Solution:

1. Start with the given equation: $2(x + 2)^2 = y - 2$

2. Add 2 to both sides to isolate $y$: $2(x + 2)^2 + 2 = y$

3. The equation for $y$ is now: $y = 2(x + 2)^2 + 2$

This is the solution for $y$ in terms of $x$.

Would you like further details or clarifications on any step? Feel free to ask!

Here are 5 related questions you might want to explore:

1. How do you graph the function $y = 2(x + 2)^2 + 2$?
2. What is the vertex of the parabola represented by $y = 2(x + 2)^2 + 2$?
3. How does the factor of 2 affect the shape of the parabola compared to $y = (x + 2)^2$?
4. Can you find the axis of symmetry for the quadratic function?
5. How would you rewrite $y = 2(x + 2)^2 + 2$ in standard form?

Tip: When solving equations involving squares, always remember to check for any additional solutions when you square both sides!