parabola --fire works!!!???!!!????!!!???????

Question

Using this equation, a firework rocket was launched:
h(t)= -4.9(t-5)² + 124

h(t) = height (meter)
t = time seconds

The max height that the fire work went to was 124 meters

it took 5 seconds for the rocket to reach that height

What is the height of the platform from which the rocket was launched from?

Answer 1

t=0 at the time of launch

so sub in 0 into the equation to get the height at the time of lanch:

h=-4.9x(0-5)^2 + 124
= -4.9x25 +124
= 1.5 meters

Answer 2

An alternate way to solve this is to multiply out the equation:

-4.9(t+5)^2 + 124
-4.9(t^2 - 10t + 25) + 124
-4.9t^2 + 49t - 122.5 + 124
-4.9t^2 + 49t + 1.5

When a position function is written in this form, the coefficient on t^2 is always the force of gravity. The coefficient on t is always the initial velocity (here 49 m/s upward), and the constant is always the initial height--which here is your answer 1.5 meters.