Math Problem Need Help? Thank You?

Question

I have a quadratic word problem. Its asking ( a rock was thrown from the top of a building, the quadratic H= -12t^2+48t+12 describes its path,for how many seconds was the rock in the air?) can someone show me how to do this? Help would be aprreciated. Thank You

the vertex will tell you the maximum heght of the rock at the time. In this case if the vertex is at (2,60) which means at 2 seconds the rock has reached its maximum height, then it starts falling. I need to know how long was the ball in the air form when it was thrown utnil it landed on the ground.

Answer 1

hi...heres the solution...
H= -12t^2+48t+12
H= -12(t^2 - 4t) + 12
H= -12(t^2-4t+4-4)+12
H= -12(t -2)^2 +48+12
H= -12(t-2)^2+60
Therefore yr vertex is at (2,60)..............

Answer 2

When it hits the ground, H = 0, so solve

-12t² + 48t + 12 = 0
-t² + 4t + 1 = 0
t² - 4t - 1 = 0
t² - 4t + 4 = 1 + 4 ......... completing square
(t - 2)² = 5
t - 2 = ±√5
t = (ignoring negative solution) 2 + √5
t = 2 + 2.24 = 4.24 seconds.

by the way, what planet is this? on Earth it would be -16t² + stuff.

Answer 3

-12t^2+48t+12
-12(t^2-4t-1)
This is not factorable into real numbers.

Answer 4

find the maximum point (the vertex)