1. **State the problem:** We are given a quadratic function $f(j) = j^2$ and need to complete the function table for $j = -1, 0, 1, 2$ by calculating $f(j)$ for each value. 2. **Formula used:** The function is defined as $f(j) = j^2$, which means for each input $j$, the output is the square of $j$. 3. **Calculate each value:** - For $j = -1$, $f(-1) = (-1)^2 = 1$ - For $j = 0$, $f(0) = 0^2 = 0$ - For $j = 1$, $f(1) = 1^2 = 1$ - For $j = 2$, $f(2) = 2^2 = 4$ 4. **Complete the table:** \begin{array}{c|c} j & f(j) \\\hline -1 & 1 \\ 0 & 0 \\ 1 & 1 \\ 2 & 4 \\ \end{array} 5. **Explanation:** Squaring a number means multiplying it by itself. Negative numbers squared become positive because a negative times a negative is positive. Zero squared is zero. Positive numbers squared remain positive. **Final answer:** The completed function table is: $j$: -1, 0, 1, 2 $f(j)$: 1, 0, 1, 4