Sketch y = x2 – 2x - 3 assuming that A and B are lying on the imaginery line, the x-axis. Find the height from which the clown begins his journey along the highwire.

Question

A clown is riding a single wheel cycle along a highwire from point A to point B. These two points are the same height, however as the clown cycles the highwire decreases in height to a minimum point 2 m above the ground. The quadratic equation used to describe this situation is y = x² – 2x - 3

 (Assume highwire represent parabolic curve).

Sketch y = x² – 2x - 3 assuming that A and B are lying on the imaginery line, the x-axis. Find the height from which the clown begins his journey along the highwire.

Answer 1

y=x²-2x-3=0; (x-3)(x+1)=0 therefore we have x-intercepts at x=-1, and x=3.

find min:

y'=2x-2=0

min @ x=1

when x=1, y=(1)²-2(1)-3=-4

we draw a line at the x-axis, and we have a minimum at x=1 of -4m

this is 2m above the ground, so what this means is that the starting point must be

6m above the ground (2m + 4m = 6m)