08.01 MC)A food packet is dropped from a helicopter and is modeled by the function f(x) = −15x2 + 6000. The graph below shows the height f(x), in feet, of the food packet at different times x, in seconds:Use the graph to determine the domain of f(x) for all viable x values based on the context.Group of answer choicesx ≤ 60000 ≤ x ≤ 20−20 ≤ x ≤ 20All real numbers

4. A student throws a bag of chips to her friend. Unfortunately, herfriend does not catch the chips, and the bag hits the ground. Thedistance from the ground (height) for the bag of chips is modeledby the function h(t) 5 216(t 2 1)2 1 20, where h is the height(distance from the ground in feet) of the chips, and t is the numberof seconds the chips are in the air.A. Graph h(t) 5 216(t 2 1)2 1 20.B. From what height are the chips being thrown? Explain howyou know.C. What is the maximum height the bag ofchips reaches while airborne? Explain howyou know.D. About how many seconds a$er the bagwas thrown did it hit the ground?E. What is the average rate of change ofheight for the interval from 0 to 12 second?What does that number represent in termsof the context?F. Based on your answer to Part E, what is the average rate of change for the interval from1.5 to 2 sec.?© Tribalium/Shutterstock.com

The graph below shows the height of a basketball after it is thrown towards a basketball hoop.Which of the following gives the domain for this function?

The function h(x)=−(x−4)2+300ℎ(𝑥)=-(𝑥-4)2+300 gives a metal ball's height above the ground in feet x𝑥 seconds after it is thrown off of a building, where 0≤x≤200≤𝑥≤20. Which of the following is the best interpretation of the vertex of the graph of y=h(x)𝑦=ℎ(𝑥) in the xy𝑥𝑦-plane?The ball's minimum height occurs at 4 secondseliminateThe ball's maximum height occurs at 4 secondseliminateThe ball is initially thrown from a height of 300 feeteliminateThe ball's minimum height is 300 feet

ProblemSuppose Jeremiah is a diver for his summer swim team. The function h(x)=−4.9x2+8x+5ℎ(𝑥)=−4.9𝑥2+8𝑥+5 represents Jeremiah's height (hℎ) in meters above the water x𝑥 seconds after he leaves the diving board.What is the initial height of the diving board?At what time did Jeremiah reach his maximum height?What was Jeremiah’s maximum height?Sketch a graph of the function. (You can use your calculator for this or create a table of values.) SolutionThe initial height of the diving board is when the time is zero.h(0)=−4.9x2+8x+5ℎ(0)=−4.9𝑥2+8𝑥+5h(0)=−4.9(0)2+8(0)+5ℎ(0)=−4.9(0)2+8(0)+5h(0)=0+0+5ℎ(0)=0+0+5h(0)=5ℎ(0)=5The initial height of the diving board is 55 m.The time at which Jeremiah reaches his maximum height is the x𝑥-coordinate of the vertex.x=−b2a𝑥=−𝑏2𝑎x=𝑥=2(2( ))x=−8−9.8𝑥=−8−9.8x=0.82𝑥=0.82 secIt took Jeremiah seconds to reach his maximum height.The maximum height was reached Jeremiah at seconds. The maximum height is the y𝑦-coordinate of the vertex.h(t)=−4.9x2+8x+5ℎ(𝑡)=−4.9𝑥2+8𝑥+5h(0.82)=−4.9(0.82)2+8(0.82)+5ℎ(0.82)=−4.9(0.82)2+8(0.82)+5h(0.82)=−3.29+6.56+5ℎ(0.82)=−3.29+6.56+5h(0.82)=8.27ℎ(0.82)=8.27 mThe maximum height reached by Jeremiah was m.CheckQuestion 8

(a)The function 𝑓(𝑡)=−5𝑡2+20𝑡+60f\left(t\right)=-5t^2+20t+60f(t)=−5t 2 +20t+60 models the approximate height of an object 𝑡tt seconds after it is launched. How many seconds does it take the object to hit the ground? (Enter only the number)