1. **Problem Statement:** (a) Complete the table for the function $$y = x^3 - 4x^2 + 12$$ at given values of $$x$$. 2. **Formula and Rules:** The function is a cubic polynomial: $$y = x^3 - 4x^2 + 12$$. To find $$y$$ for each $$x$$, substitute the value of $$x$$ into the expression and simplify. 3. **Calculations:** - For $$x = -2$$: $$y = (-2)^3 - 4(-2)^2 + 12 = -8 - 4(4) + 12 = -8 - 16 + 12 = -12$$ - For $$x = -1$$: $$y = (-1)^3 - 4(-1)^2 + 12 = -1 - 4(1) + 12 = -1 - 4 + 12 = 7$$ - For $$x = 0$$: $$y = 0^3 - 4(0)^2 + 12 = 0 - 0 + 12 = 12$$ - For $$x = 1$$: $$y = 1^3 - 4(1)^2 + 12 = 1 - 4 + 12 = 9$$ - For $$x = 2$$: $$y = 2^3 - 4(2)^2 + 12 = 8 - 16 + 12 = 4$$ - For $$x = 3$$: $$y = 3^3 - 4(3)^2 + 12 = 27 - 36 + 12 = 3$$ - For $$x = 4$$: $$y = 4^3 - 4(4)^2 + 12 = 64 - 64 + 12 = 12$$ 4. **Answer:** The completed table is: | x | -2 | -1 | 0 | 1 | 2 | 3 | 4 | |----|----|----|----|----|----|----|----| | y | -12| 7 | 12 | 9 | 4 | 3 | 12 | This matches the values given, confirming correctness. **Final answer:** The table is complete as given.