1. **State the problem:** We need to complete the table for the quadratic expression $x^2 - 13x + 42$ when $x = -6$. 2. **Recall the formula:** The expression is $x^2 - 13x + 42$. To fill the table, we calculate $x^2$ and then the full expression value for the given $x$. 3. **Calculate $x^2$ when $x = -6$:** $$(-6)^2 = 36$$ 4. **Calculate the full expression value when $x = -6$:** $$(-6)^2 - 13(-6) + 42 = 36 + 78 + 42$$ 5. **Simplify the sum:** $$36 + 78 = 114$$ $$114 + 42 = 156$$ 6. **Fill the table values:** - For $x = -6$, $x^2 = 36$ - The expression value is $156$ **Final answer:** When $x = -6$, $x^2 = 36$ and $x^2 - 13x + 42 = 156$.