SOLUTION: A parabolic shaped-canal is 8m wide and 2m deep at the center, write a defining equation for the parabolic- shaped canal. Use the equation to find the canal's depth every meter.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A parabolic shaped-canal is 8m wide and 2m deep at the center, write a defining equation for the parabolic- shaped canal. Use the equation to find the canal's depth every meter.       Log On


   

Question 1143669: A parabolic shaped-canal is 8m wide and 2m deep at the center, write a defining equation for the parabolic- shaped canal. Use the equation to find the canal's depth every meter.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You can put the vertex at the point ( 0, -2 ) on the y-axis.
The canal will then go through points ( 4,0 ) and ( -4,0 )
which is maximum width
The general equation is:
+y+=++a%2Ax%5E2+%2B+b%2Ax+%2B+c++
------------------------------
( 0,-2 )
+-2+=+a%2A0%5E2+%2B+b%2A0+%2B+c+
+-2+=+c+
---------------
( 4,0 )
+0+=+a%2A4%5E2+%2B+b%2A4+-+2+
+0+=+16a+%2B+4b+-+2+
(1) +8a+%2B+2b+=+1+
----------------------
(-4,0 )
+0+=+a%2A%28-4%29%5E2+%2B+b%2A%28-4%29+-+2+
+0+=+16a+-+4b+-+2+
(2) +8a+-+2b+=+1+
----------------------
Add (1) and (2)
+8a+%2B+2b+=+1+
+8a+-+2b+=+1+
-------------------
+16a+=+2+
+a+=+1%2F8+
and
(1) +8a+%2B+2b+=+1+
(1) +8%2A%281%2F8%29+%2B+2b+=+1+
(1) +1+%2B+2b+=+1+
(1) +2b+=+0+
(1) +b+=+0+
-------------------
The equation is:
+y+=+%281%2F8%29%2Ax%5E2+-+2+
-------------------------
Every meter, the depths are:
(-4, 0 )
( -3, y[1] )
( -2, y[2] )
( -1, y[3] )
( 0. y[4] )
( 1, y[3] )
( 2, y[2] )
( 3, y[1] )
( 4, 0 )
----------------
( -3, y[1] )
+y%5B1%5D+=+%281%2F8%29%2A%28-3%29%5E2+-+2+
+y%5B1%5D+=+9%2F8+-+16%2F8+
+y%5B1%5D+=+-7%2F8+
---------------------
You can continue the process