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pre-cal Math help, can you tell me if this question makes sense or not? please explain what they mean and how to solve this type of question

the question is: Layla bought a toy rocket. she calculated that the rocket's height as a function of time can be represented by h(t)=-16t2 + 4t where h is height in feet and t is time in seconds. if the shuttle follows this, how long will it be in the air? they give no height, and do not include distance in the equation or weight of the object. how can this equation work? if the shuttle gets 0 feet in the air, won't it just be in the air for 0 seconds? yet they say the answer is .25 seconds!

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The function shows the position of the shuttle at each point in time. At t=0, the shuttle is indeed on the ground, but it is on its way upwards.

You solve this by setting the height = 0 and finding the solutions to the equation. The first zero is launch, the second is landing. If there were more zeroes, they would not matter because the shuttle has already landed.

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H(t)=-16t^2+4t.
-4t( 4t-1)=0. T=0 and t=1/4.
So the rocket is on the ground at 0 sec and 1/4 sec bc the height was set equal to zero. Not in the air very long!! Ha! If you graph it, set your domain from zero to .25 and the range from 0 to 1/2.....you'll see the distance change.

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