1) A tank is takingartillery practice on Ft. Bliss Army Base. It fires shells at
ID: 3089623 • Letter: 1
Question
1) A tank is takingartillery practice on Ft. Bliss Army Base. It fires shells at anangle so that the shells trajectories follow the parabolaf (x) = -0.002x2 +4x; where xis horizontal distance andf (x) is verticaldistance, both measured in feet.
a) Put the quadraticin vertex form by completing the square. Graph it and state thelocation of the vertex. Where do the shells hit theground?
b) The tank thenmoves 500 feet forward (to the right) and climbs a hill that is 100feet high. It fires again from this location. Find the functionthat gives the paths of the shells now. Describe it in termsof shifting the original function. Where do the shells hit theground?
c) Suppose the tankturns around 180 degrees from its position on the hill and firesfrom there. Find the equation of the shells. paths and describe it.Again, determine where the shells hit the ground.
Explanation / Answer
y=-.002(x^2 -2000x) then you take the term infront of the x and you half it thensquare it;
(-2000/2)^2 =1 000 000 you then take this number and you add it and subtract it butkeep them seperate
y=-.002[x^2-2000x+1000 000 -100000] you can then factor that to be;
y=-.002[(x+1000)^2 -100 000] that's the complpeted square
mooving the tank 500 ft to the right is adding 500 to x, sojust put in (x+500) wherever there was an z, this shifts thefunction to the right.
then insert for y;(100+y) which shifts the graph up by100 then for the 180 degree switch; you can make the xnegtive
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