SOLUTION: The function s = -16t^2 + 64t + 512 gives the position (in feet) of a rocket fired upward from an initial height of 512 feet above the ground a)How long does it take for the roc

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Question 735792: The function s = -16t^2 + 64t + 512 gives the position (in feet) of a rocket fired upward from an initial height of 512 feet above the ground
a)How long does it take for the rocket to reach its maximum height?
b)What is the maximum height obtained by the rocket?
c)How long does it take for the rocket to reach the ground?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The equation has the general form +y+=+ax%5E2+%2B+b%2Ax+%2B+c+
The x-coordinate of the vertex is at +x+=+-b%2F%282a%29+
In the given equation:
+t+=+-64+%2F+%28+2%2A%28-16%29%29+
+t+=+2+
(a) The rocket takes 2 sec to reach maximum height
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Find s when +t+=+2+
+s+=+-16t%5E2+%2B+64t+%2B+512+
+s+=+-16%2A2%5E2+%2B+64%2A2+%2B+512+
+s+=+-64+%2B+128+%2B+512+
+s+=+576+
(b) At the vertex, the height is 576 ft above ground
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Find +t+ when +s+=+0+
+0+=+-16t%5E2+%2B+64t+%2B+512+
+-t%5E2+%2B+4t+%2B+32+
+%28+-t+%2B+8+%29%2A%28+t+%2B+4+%29+ ( I could see these were factors )
+t+=+8+ ( ignore other solution-can't have negative time )
(c) In 8 sec, the rocket reaches the ground
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Here's the plot:
+graph%28+400%2C+400%2C+-3%2C+10%2C+-30%2C+625%2C+-16x%5E2+%2B+64x+%2B+512+%29+