The vertical distance of a given point on Mount HImalayas is km. It has a horizontal distance of km from a reference point O. A plane flew above Mount Himalayas and its average vertical height was given by km, where k is a real number. The horizontal distance of the plane was also x km from O.
Given that the vertical safety distance between any plane and Mount Himalayas should be at least 1 km at any point in time, can the plane meet the safety requirements at all times? Explain your answer with the help of mathematical concepts learnt in the topic of quadratic functions.