Question

The function h represents the height of an object t seconds after it is launched into the air. The function is

defined by h(t)= -5t² + 20t+18. Height is measured in meters.

After how many seconds does the object reach a height of 33 meters?

Answer 1

Explanation:

h(t) = -5t² + 20t + 18

this is a parabola (the curve an object follows when thrown up into the air and then falling back down).

and as such it will most likely have 2 solutions (one for when going up, and one for when falling back down again).

33 = -5t² + 20t + 18

15 = -5t² + 20t

-3 = t² - 4t

t² - 4t + 3 = 0

the solution of such a quadratic equation is

t = (-b ±sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -4

c = 3

t = (4 ±sqrt(16 - 4×1×3))/(2×1) = (4 ±sqrt(16-12))/2 =

= (4 ±sqrt(4))/2 = (4 ± 2)/2

t1 = (4+2)/2 = 6/2 = 3

t2 = (4-2)/2 = 2/2 = 1

the object reaches the height of 33 m first after 1 second (while going up), and then again after 3 seconds (while falling down again).