To solve this problem is useful to look at the graph of the function and identify if there is a maximum or minimum point.
The function is:
[tex]g(x)=2x^2-16x+31[/tex]
The graph of this function we can find it using any graphing software and looks as follows:
As we can see, the function has a minimum, because there is a lower point in the graph.
Does the function have a minimum or maximum? Answer: Minimum.
To find the function minimum value, we consider the black point shown in the graph (the minimum point) it is at:
[tex](4,-1)[/tex]
-1 is the function's minimum value, and x=4 is where the minimum value occurs. So we can solve the next two questions:
what's the functions minimum or maximum value? Answer: -1
Where does the minimum or maximum value occur? Answer: 4
