The given function is:

$f(x) = 2(x - 3)^2 + 4$

You are asked to rewrite it in the form $f(x) = ax^2 + bx + c$.

Steps to simplify:

1. Expand the squared term $(x - 3)^2$:

$(x - 3)^2 = x^2 - 6x + 9$

2. Substitute this back into the original function:

$f(x) = 2(x^2 - 6x + 9) + 4$

3. Distribute the $2$ through the terms inside the parentheses:

$f(x) = 2x^2 - 12x + 18 + 4$

4. Combine like terms:

$f(x) = 2x^2 - 12x + 22$

So, the function in the form $ax^2 + bx + c$ is:

$f(x) = 2x^2 - 12x + 22$

Would you like more details or have any further questions? Here are some related questions:

1. How do you expand $(x - a)^2$ in general?
2. What is the significance of completing the square in this context?
3. How would you factor $2x^2 - 12x + 22$?
4. How does the vertex form of a quadratic function relate to the standard form?
5. Can the same method be applied to other forms of quadratic functions?

Tip: Expanding squared binomials is essential when transforming between different forms of quadratic equations!