Ive been stuck on this for so long and i just keep getting frustrated can someone walkme through this? i did letter a which i believe is h(t)=-16t^2+150 o t+100 o and the height of the building is 100 feet. one of the fireworks is launched from the top of the building with an initial upward velocity of 150 ft/sec. a. what is the equation for this situation? b. when will the firework land if it does not explode? c. make a table for this situation so that it shows the height from time t = 0 until it hits the ground. d. calculate the axis of symmetry. e. calculate the coordinates of the vertex. f. explain why negative values for t and h t( ) do not make sense for this

For firework launched from height 100ft with initial velocity 150ft/sec, equation made is correct

(a) equation will be

(b) Now we have to see when it will land. At land or ground level height h will be equal to 0. So simply plug 0 in h place in equation made in part (a)

Now we have to solve this quadratic. We will use quadratic formula method to solve this equation.

a = -16, b = 150, c = 100.

Plugging these values in quadratic formula we get

time cannot be negative so we will drop this answer

then

So 10 seconds is the answer for this

(c) To make table simply plug various value for t like t =0, 2, 4, 6, 8 till 10. Plug values in equation mad in part (a) and find h value for each t as shown

For t =0 seconds,

For t =2 seconds,

For t =4 seconds,

For t =6 seconds,

For t =8 seconds,

For t =10 seconds,

(d) Axis of symmetry is given by formula

t = 4.6875 is axis of symmetry line

(e) x-coordinate of vertex is again given by formula

so t = 4.6875

then to find y coordinate we will plug this value of t as 4.6875 in equation made in part (a)

For t =4.6875,

so vertex is at (4.6875, 451.563)

(f) As the firework is launched so in starting time is t=0, we cannot have time before t=0 (negative values) practically. Also we cannnot have firework going down into the ground so we cannot have h value negative physically.