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$f(x)=\

$$\begin{cases}3x + 9&\\text{for }x\\leq -5\\\\-(x - 1)^2 - 3&\\text{for }x\\geq -1\\end{cases}$$

$
find $f(0)$

Explanation:

Step1: Identify correct function piece

Check that $0 \geq -1$, so use $f(x) = -(x-1)^2 - 3$.

Step2: Substitute $x=0$ into the function

$$f(0) = -(0-1)^2 - 3$$

Step3: Simplify the expression

First calculate $(0-1)^2 = (-1)^2 = 1$, then:
$$f(0) = -1 - 3 = -4$$

Answer:

$-4$