The direction in whythe graph opens

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.

ou would have 12 of each