The function f(t) = 4t2 − 8t + 8 shows the height from the ground f(t), in meters, of a roller coaster car at different times t. Write f(t) in the vertex form a(x − h)2 + k, where a, h, and k are integers, and interpret the vertex of f(t). f(t) = 4(t − 1)2 + 4; the minimum height of the roller coaster is 4 meters from the ground f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 4 meters from the ground f(t) = 4(t − 1)2 + 4; the minimum height of the roller coaster is 1 meter from the ground f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 2 meters from the ground

Select the correct answer from each drop-down menu.A roller coaster moves along an inclined linear path before it reaches its maximum height. The car moves at a constant speed and gains 4 meters in height every 3 seconds.The slope of the line that represents the height of the car in meters in terms of time in seconds is .If the car takes 54 seconds to reach the maximum height, then the maximum height above the ground is meters.

The height of a roller coaster at a given time is modeled by the polynomial function ℎ(𝑡)=(−0.01𝑡3+0.35𝑡2−3.5𝑡+10)(𝑡+5)2(𝑡−5)(𝑡+1)(2−𝑡)3h(t)=(−0.01t 3 +0.35t 2 −3.5t+10)(t+5) 2 (t−5)(t+1)(2−t) 3 , where t represents time in seconds. Find the turning point(s) of the height function.6758

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

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

Instructions: Given the function, state the vertex.y=−3(x+4)2−8