Complete each sentence. The vertex of the graph of g(x) = 3|x| + 4 is Choose... . The graph opens Choose... .

Question

Options for choose #1

(4, 0) 

(0, –4) 

(0, 4) 

(–4, 0) 

Options for choose #2

Upward

Downward

Answer 1

First, we must know what the graph y= IxI looks like because this is the standard graph that we are manipulating. The graph of y= IxI looks like an upward V where the vertex (the point of the V) is at (0,0). Now, we look at what changes are happening to the x. The change on the x is that it is being multiplied by 3. Because the vertex is at (0,0) the multiplication of 3 does not affect the vertex, which means the x value will stay the same. In addition, because the x is being multiplied by a positive number which means that it will not flip the opening of the curve. This means that the new curve will also open upward. The change on the y is that 4 is being added to the 3x. If we apply this to the vertex, the y-value will now be 4. That leaves us with the vertex at the point (0,4).