Answer: upward
Explanation:
Since the absolute value is positive (or zero), the function will be a positive value (or zero) plus 12, which is, of course, a positive value (greater than or equal to 12).
That tells you that the function will never go below the x-axys (actually never below 12). Hence, you can be sure that the function has to open upward.
The attached graph shows this result.
To draw that graph, I recommend to make a brief analysis and a table:
1) The minimum value is when the absolute value is zero, and the function is 0 + 12 = 12. That happens when x = 0: |0 + 0| + 12 = 0 + 12 = 12.
That means that the vertex is (0,12).
2) Now choose some values to draw the graph:
Table
x f(x) = |∛x + 2x | + 12
- 27 | ∛(-27) + 2(-27) | + 12 = 69
- 8 | ∛(-8) + 2(-8) | + 12 = 30
-1 | ∛(-1) + 2(-1) | + 12 = 15
0 | 0 | + 12 = 12
1 15
8 30
27 69
With that you can draw the table. Of course you can also use a graphing calculator, which I did. See the graph attached. It shows clearly the direction in which the graph opens is upward.
