SOLUTION: A frog leaps 2 feet horizontally. The highest point in the jump is 1/2 foot. Assume the frog starts at (0, 0). What quadratic function models the path of the jump?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A frog leaps 2 feet horizontally. The highest point in the jump is 1/2 foot. Assume the frog starts at (0, 0). What quadratic function models the path of the jump?      Log On


   

Question 910154: A frog leaps 2 feet horizontally. The highest point in the jump is 1/2 foot. Assume the frog starts at (0, 0). What quadratic function models the path of the jump?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The general function is:
+y+=+a%2Ax%5E2+%2B+b%2Ax+
Note that if +x+=+0+ then
+y+=+0+, so that gives you
the point (0,0)
-------------------------
You also are given the point
(2,0), so
+0+=+a%2A2%5E2+%2B+b%2A2+
+4a+=+-2b+
+a+=+-b%2F2+
-------------------------
The formula for the x-coordinate of the
highest point is:
+x%5Bmax%5D+=+-b%2F%282a%29+
By substitution:
+x%5Bmax%5D+=+%28+-b%2F2+%29%2A%28+2%2F%28-b%29%29+
+x%5Bmax%5D+=+1+
--------------------
+y%5Bmax%5D+=+a%2A1%5E2+%2B+b%2A1+
+y%5Bmax%5D+=+a+%2B+b+
+1%2F2+=+a+%2B+b+
and, since
+a+=+-b%2F2+
+1%2F2+=+-b%2F2+%2B+b+
+1%2F2+=+b%2F2+
+b+=+1+
and
+a+=+-b%2F2+
+a+=+-1%2F2+
---------------
So, the equation is:
+y+=+%28-1%2F2%29%2Ax%5E2+%2B+x+
---------------------
Here is the plot:
+graph%28+400%2C+400%2C+-.5%2C+3%2C+-1%2C+2%2C++%28-1%2F2%29%2Ax%5E2+%2B+x+%29+