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Question 1026984: a firework is launched from the top of a 216ft building with an initial upward velocity of 150 ft/sec
h(t)=-16t^2+vt+h
t=time, h is initial height, v is the initial velocity in feet per second
1.what is the equation for this situation
2.when will the firework land if it does not explode
3.show a table for this situation so that it shows the height from time t=0 until it hits the ground
4.calculate the axis of symmetry
5.calculate the coordinates of the vertex
6.explain why negative values of t and h(t) do not make sense for this problem
7. graph the situation
on #3 for the table, I do not know how to solve for the 0 or for 1,2,3,4,5 etc..... because it is after the = sign. So PLEASE show work. ALSO,how did you calculate the axis of symmetry and the coordinates of vertex? I have a TI-84 graphing calculator and can not get #7 to graph on it. And I do not know why? And in #1, it is supposed to be -16t^2 and I have asked this same question twice. Both times the same tutor used -15t^2. I do not know if this was used on the problems to get the answers for the symmetry and vertex. If so, then those are not right either....... That's why I resubmitted this question. Besides, I don't just need the answers..... I need to know how to do it so I can show my daughter and she can know for the test....... Thank You!
Found 2 solutions by sroberts978, MathTherapy:
Answer by sroberts978(2)   (Show Source):
You can put this solution on YOUR website! a firework is launched from the top of a 216ft building with an initial upward velocity of 150 ft/sec
h(t)=-16t^2+vt+h
t=time, h is initial height, v is the initial velocity in feet per second
1.what is the equation for this situation
2.when will the firework land if it does not explode
3.show a table for this situation so that it shows the height from time t=0 until it hits the ground
4.calculate the axis of symmetry
5.calculate the coordinates of the vertex
6.explain why negative values of t and h(t) do not make sense for this problem
7. graph the situation
on #3 for the table, I do not know how to solve for the 0 or for 1,2,3,4,5 etc..... because it is after the = sign. So PLEASE show work. ALSO,how did you calculate the axis of symmetry and the coordinates of vertex? I have a TI-84 graphing calculator and can not get #7 to graph on it. And I do not know why? And in #1, it is supposed to be -16t^2 and I have asked this same question twice. Both times the same tutor used -15t^2. I do not know if this was used on the problems to get the answers for the symmetry and vertex. If so, then those are not right either....... That's why I resubmitted this question. Besides, I don't just need the answers..... I need to know how to do it so I can show my daughter and she can know for the test....... Thank You!
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
a firework is launched from the top of a 216ft building with an initial upward velocity of 150 ft/sec
h(t)=-16t^2+vt+h
t=time, h is initial height, v is the initial velocity in feet per second
1.what is the equation for this situation
2.when will the firework land if it does not explode
3.show a table for this situation so that it shows the height from time t=0 until it hits the ground
4.calculate the axis of symmetry
5.calculate the coordinates of the vertex
6.explain why negative values of t and h(t) do not make sense for this problem
7. graph the situation
on #3 for the table, I do not know how to solve for the 0 or for 1,2,3,4,5 etc..... because it is after the = sign. So PLEASE show work. ALSO,how did you calculate the axis of symmetry and the coordinates of vertex? I have a TI-84 graphing calculator and can not get #7 to graph on it. And I do not know why? And in #1, it is supposed to be -16t^2 and I have asked this same question twice. Both times the same tutor used -15t^2. I do not know if this was used on the problems to get the answers for the symmetry and vertex. If so, then those are not right either....... That's why I resubmitted this question. Besides, I don't just need the answers..... I need to know how to do it so I can show my daughter and she can know for the test....... Thank You!
You ask for a LOT!
I’ll try to guide you
1. 
 --------- Substituting given values: 216 for h; and 150 for v
2. The firework will land when h (height) = 0. Substitute 0 for h (t) to get the roots/zeros, ignoring any negative (< 0) values.
3. You need to create this table yourself
4. The axis of symmetry is at t = - , or  . You can calculate this!
5. Substitute the value of the axis of symmetry (no. 4) and determine h(axis of symmetry). The values of the axis of symmetry, and
h(axis of symmetry) will be the coordinates of the vertex
6. Negative values of t suggest NEGATIVE time. There is no such thing as negative time. The same goes for h(t), or height, which
can never be negative (< 0).
7. You need to pick up your TI-84 and graph equation in no. 1, entering: 
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