1. **Problem Statement:** Evaluate the piecewise function $$f(x) = \begin{cases} -2x + 3, & x < -1 \\ 2x^2, & x \geq -1 \end{cases}$$ at the given values of $x$: 0, -4, and 5. 2. **Step 1: Evaluate $f(0)$** Since $0 \geq -1$, use the second piece: $f(0) = 2(0)^2 = 0$. 3. **Step 2: Evaluate $f(-4)$** Since $-4 < -1$, use the first piece: $f(-4) = -2(-4) + 3 = 8 + 3 = 11$. 4. **Step 3: Evaluate $f(5)$** Since $5 \geq -1$, use the second piece: $f(5) = 2(5)^2 = 2 \times 25 = 50$. **Final answers:** - $f(0) = 0$ - $f(-4) = 11$ - $f(5) = 50$