The height (in metres) of a parabolic arch above the ground at a horizontal distance…

MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

The height (in metres) of a parabolic arch above the ground at a horizontal distance

x

metres from one end is given by

h(x)=x^{2}-6x+t,

where

t

is a real constant and

x

may take any real value. (i) State the condition that must be satisfied so that the arch never touches the ground for any real value of

x

. (ii) Using the condition in part (i), find the range of values of

t

for which the arch remains strictly above the ground at all points.