Respuesta :

Answer:

(0,0)

Step-by-step explanation:

Given that f(x) = |x^(1/3)+2x|+12

Since modulus remains the same value for values >0 and becomes negative for values less than 0, i.e. |x| =x, if x >0 and

                                               =-x, if x<0

Using this we find f(x) = x^(1/3)+2x+12 if x>0 and

                                      =-x^(1/3)-2x+12, if x<0

f(0) = 12

Thus the given f(x) can be defined as a piecewise function with split at x =0

and f(0) = 12

Take any other value say -1 and 1 on either side of 0

f(-1) = -(-1-2)+12>0 and

f(1) = 1+2+12>0

Hence all values of f(x) have range >=0

The minimum value of f(x) = 0 and there is only one minimum here.

Hence vertex of the graph = (0,0)

Edufirst

Answer: the vertex is (0,12).


Explanation:


You can find both the graph and how I determined the vertex is this link https://brainly.com/question/11448853.


There, I explain that, since the absolute value is positive (or zero), the function will be a positive value (or zero) plus 12, which is a value greater than or equal to 12.


The minimum value, then, is when the absolute value is zero, which happens when x = 0, and it is 12. So, the vertex is (0,12).


The attached graph shows this result.


You can draw such graph by using a table with some points.


This is the table that I did:


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


You may draw the graph with those values or you can use a graphing calculator, which I did. See the graph attached. It shows clearly that the vertex is (0,12).

Ver imagen Edufirst

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