To transform the quadratic function into standard form, you need to expand and simplify the expression. The given function is:

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

Step 1: Expand the squared term $(x + 6)^2$

$(x + 6)^2 = x^2 + 12x + 36$

Step 2: Multiply by $-3$

$-3(x^2 + 12x + 36) = -3x^2 - 36x - 108$

Step 3: Add the constant term $-9$

$f(x) = -3x^2 - 36x - 108 - 9$

Step 4: Simplify

$f(x) = -3x^2 - 36x - 117$

Thus, the quadratic function in standard form is:

$f(x) = -3x^2 - 36x - 117$

Would you like details on the expansion or have any questions?

Here are 5 related questions to consider:

1. How can you identify the vertex of a quadratic function from its standard form?
2. What is the axis of symmetry for this quadratic function?
3. How does the transformation of a quadratic function affect its graph?
4. Can you find the roots of this quadratic function using the quadratic formula?
5. What is the significance of the coefficient of $x^2$ in the standard form?

Tip: The vertex form of a quadratic function, like the one you started with, reveals the vertex directly as $(-h, k)$ from $(x + h)^2 + k$.