Analytic Goemetry
posted by AJ .
Find the equation of the parabola with axis parallel to the xaxis and passing through (3/2,1),(5,0) and (1,2).

In this case we don't know anything about the vertex, so we have to use the more general equation of the form
x = ay^2 + by + c
using (3/2 , 1)  3/2 = a + b + c
using (5,0 )  5 = 0+0+c or c=5
using (1,2)  1 = 4a + 2b + c
from the 2nd we know c=5
so in the first: a + b = 7/2 (#1)
in the 3rd : 4a + 2b = 6 or 2a + b = 3 (#3)
subtract #3  #1 > a = 1/2
back in #1 :
1/2 + b = 7/2  b = 4
so equation is
x = (1/2)y^2  4y + 5
Check to see of all 3 points satisfy this equation.
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