SOLUTION: A ball is thrown across a playing field. Its path is given by the equation y = −0.005 x^2 + x + 6 , where x is the distance the ball has traveled horizontally, and y is its h

Algebra ->  Finance -> SOLUTION: A ball is thrown across a playing field. Its path is given by the equation y = −0.005 x^2 + x + 6 , where x is the distance the ball has traveled horizontally, and y is its h      Log On


   

Question 906061: A ball is thrown across a playing field. Its path is given by the equation y = −0.005 x^2 + x + 6 , where x is the distance the ball has traveled horizontally, and y is its height above ground level, both measured in feet.
(a) What is the maximum height attained by the ball?

(b) How far has it traveled horizontally when it hits the ground?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+y+=+-.005%2A+x%5E2+%2B+x+%2B+6+
Find +y%5Bmax%5D+
The x-coordinate of the vertex is located at
+x%5Bmax%5D+=+-b%2F%282a%29+
+x%5Bmax%5D+=+-1+%2F+%28+2%2A%28-.005%29+%29+
+x%5Bmax%5D+=+1%2F.01+
+x%5Bmax%5D+=+100+
and
+y%5Bmax%5D+=+-.005%2A+100%5E2+%2B+100+%2B+6+
+y%5Bmax%5D+=+-50+%2B+106+
+y%5Bmax%5D+=+56+
(a)
The max height is 56 ft
(b)
It hits the ground when +y+=+0+
+-.005%2A+x%5E2+%2B+x+%2B+6+=+0+
Multiply both sides by +-200+
+x%5E2+-+200x+-+1200+=+0+
+x%5E2+-+200x+=+1200+
+x%5E2+-+200x+%2B+%28+200%2F2+%29%5E2+=+1200+%2B+%28+200%2F2+%29%5E2+
+x%5E2+-+200x+%2B+10000+=+11200+
+%28+x+-+100+%29%5E2+=+11200+
+x++-+100+=+105.83+
+x+=+205.83+
When it hits the ground, it has traveled 205.83 ft
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Here's the plot:
+graph%28+600%2C+600%2C+-10%2C+220%2C+-5%2C+60%2C+-.005%2Ax%5E2+%2B+x+%2B+6+%29+