2025 NASS PRELIMS P1 Q2

The equation of a quadratic curve is given by \(y=-x^2+px-17\) and it has a maximum point \((4,q)\) where \(p\) and \(q\) are constants.

1. By expressing \(y\) in the form of \(-(x-a)^2+b\), find the value of \(p\) and of \(q\).[4]
2. Hence, write down the nature of the turning point of \(y=\dfrac{5}{-x^2+px-17}\) and state the coordinates of the turning point.[2]