Question

Part A
Create a function to model the height of a firework when shot in the air. Explain whether the function will have a maximum or a minimum value.

Part B
Using the equation representing the height of the firework (h = -16t2 + v0t + h0), algebraically determine the extreme value of f(t) by completing the square and finding the vertex. Interpret what the value represents in this situation.

Part C (graph it for me on desmo and then attatch the photo)
Graph the quadratic function that represents the height of the firework. Determine an appropriate domain and range for this function, and use those as x and y minimums and maximums.

Part D
Determine the zeros of the function from the graph or algebraically (by factoring). Explain what these zeros mean in this situation.

Part E
Type the correct answer in the box.
Determine the average rate of change for the quadratic function representing the height of the firework with regard to time over the interval [0,4].

average rate of change = _____ ft/s

Part F
What will the height of the firework be 3 seconds after the launch? How many seconds after launch will it take for the firework to fall to the same height again?

Part G
For the safety of the audience, the fireworks should be set to explode at least 450 feet above the ground. The length of the second fuse in a mortar firework controls when the firework explodes. The fireworks company has these four fuses available:

Fuse A: The firework will explode in 1 to 3 seconds.
Fuse B: The firework will explode in 3 to 5 seconds.
Fuse C: The firework will explode in 6 to 8 seconds.
Fuse D: The firework will explode in 8 to 10 seconds.
Which fuse should the company use for your fireworks display, and why?

Answer 1

Please help with what you can. Anything helps

Answer 2

I need help. I can't go on with my work until i finish this question first.

Answer 3

k

Answer 4

@extrinix

Answer 5

@snowflake0531

Answer 6

Anyone?

Answer 7

i like ariana grandaaaaaaa

Answer 8

You truncated the first part of the question so I can't really help you there.
For completion of the square in part B:
\[h = -16t^2 + v_0t + h_0\]
You want to factor out the common term first in the quadratic term
\[h = -16(t^2 - v_0t/16) + h_0\]
Next, "complete the square" by adding the correct term
\[h = -16(t^2 - v_0*t/16+v_0/1024) + h_0+16*v_0/1024\]
Re-write as a square expression:
\[h = -16(t^2-v_0/32)^2 + h_0+v_0/64\]
The vertex can be found from inspection:
\[(v_0/32,\text{ }h_0+v_0/64)\]
The value represents the peak height of firework - when it reaches its highest point.

Answer 9

I think you're supposed to put in actual numbers for \(v_0\) and \(h_0\), but they're probably in the first part of the problem that got omitted. If you can include the first part I can probably give you exact numbers for the vertex.

Answer 10

Do you still need help with this?