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**acc100jt** The vertical distance of a given point on Mount HImalayas is $\displaystyle (-x^2+4x+6)$ km. It has a horizontal distance of $\displaystyle x$km from a reference point *O*. A plane flew above Mount Himalayas and its average vertical height was given by $\displaystyle (\frac{1}{4}x^2+kx+\frac{5}{4}k)$ 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.