Which of the graphs below is a sketch of \[y = \frac{1}{4xx^25}\; ?\]




We can complete the square. We have \(4xx^25 = (x^24x) 5 = ((x2)^24)5 = (x2)^2+45 = (x2)^21\).
So the graph is \[y = \frac{1}{(x2)^21},\] which shows the function is always negative, and has a minimum value of \(y=1\) at \(x=2\).
Hence the correct graph is c.