SOLUTION: A gush of wind sends dandelion seeds through the air. The path of the seeds can be modelled by the equation, h = -4.9t2 + 4t + 8 where h represents the height in centimeters and

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: A gush of wind sends dandelion seeds through the air. The path of the seeds can be modelled by the equation, h = -4.9t2 + 4t + 8 where h represents the height in centimeters and      Log On


   



Question 607060: A gush of wind sends dandelion seeds through the
air. The path of the seeds can be modelled by the
equation, h = -4.9t2 + 4t + 8 where h represents
the height in centimeters and t is time measured in
seconds. What is the highest height the seeds will
reach?
solve please

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The minus sign in front of the t%5E2
term tells me that this 2nd degree
curve has a maximum and not a minimum.
The t-coordinate of the vertex ( maximum )
is at +t%5Bv%5D+=+-b%2F%282a%29+ when the
form is +at%5E2+%2B+bt+%2B+c+
+a+=+-4.9+
+b+=+4+
+t%5Bv%5D+=+-4%2F%282%2A%28-4.9%29%29+
+t%5Bv%5D+=+2%2F4.9+
+t%5Bv%5D+=+.4082+
Plug this back into equation to find +h%28.4082%29+
+h%28t%29+=+-4.9t%5E2+%2B+4t+%2B+8+
+h%28.4082%29+=+-4.9%2A%28.4082%29%5E2+%2B+4%2A.4082+%2B+8+
+h%28.4082%29+=+-4.9%2A.1666+%2B+1.6326+%2B+8+
+h%28.4082%29+=+-.8163+%2B+1.6326+%2B+8+
+h%28.4082%29+=+-.8163+%2B+1.6326+%2B+8+
+h%28.4082%29+=+8.8163+
The greatest height in cm is 8.8163 cm
here's a plot:
( ignore the negative values of t )
+graph%28+400%2C+400%2C+-2%2C+4%2C+-2%2C+10%2C+-4.9x%5E2+%2B+4x+%2B+8+%29+