Review question

# Can we identify the right sketch graph of this reciprocal function? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5868

## Solution

Which of the graphs below is a sketch of $y = \frac{1}{4x-x^2-5}\; ?$

We can complete the square. We have $4x-x^2-5 = -(x^2-4x) -5 = -((x-2)^2-4)-5 = -(x-2)^2+4-5 = -(x-2)^2-1$.

So the graph is $y = \frac{1}{-(x-2)^2-1},$ which shows the function is always negative, and has a minimum value of $y=-1$ at $x=2$.

Hence the correct graph is c.