1. Suppose the height, h, in feet, of a trampolinist above the ground during one bounce is modelled by the quadratic function h(t) = -16t2 + 42t + 3.75 . For what period of time is the trampolinist at least 22 ft above the ground? Round your answers to the nearest hundredth. (2 marks)

Question

2. The length of a rectangle is 5 cm more than its width. What are the possible dimensions of the rectangle if the area must be at least 84 cm2? (2 marks)
3. A square storage area measures 10 m on a side. By how much must each side be shortened to decrease this area to less than half the original area? (3 marks - show your work)

Answer 1

parabola opens down (sheds water)
when is it between the vertex and 22 feet?

16 t^2 - 42 t - 3.75 = -22

16 t^2 - 42 t + 18.25 = 0

t = [ 42 +/- sqrt (1764 - 1168) ] / 32

t = [ 42 +/- 24.4 ] /32

t = .55 to 2.07 seconds

Answer 2

w(w+5) >/= 84

w^2 + 5 w - 84 >/= 0
solve for zero, anything bigger works

w = [ -5 +/- sqrt(25 + 336) ]/ 2

w = [ -5 + 19 ]/2 = 7
then L = 12
so anything at least 7 by 12

Answer 3

divide length dimension by sqrt 2 to get half the area