SOLUTION: Find the equation of a parabola that passes through the points (-2,3), (-1,1) and (1,9).

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find the equation of a parabola that passes through the points (-2,3), (-1,1) and (1,9).      Log On


   



Question 318422: Find the equation of a parabola that passes through the points (-2,3), (-1,1) and (1,9).
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The general equation for a parabola is,
y=ax%5E2%2Bbx%2Bc
1.(-2,3):3=4a-2b%2Bc
2.(-1,1):1=+a+-+b+%2B+c
3.(1,9):9=+a+%2B+b+%2B+c+
Solve for a,b,c using elimination, substitution, or matrix methods.
Solve for b by subtracting eq. 2 and eq. 3,
a-b%2Bc-a-b-c=1-9
-2b=-8
highlight%28b=4%29
Then substituting for b, subtract eq. 3 from eq. 1,
4a+-+8+%2B+c+-+a+-+4+-+c=3+-+9
3a-12=-6
3a=6
highlight%28a=2%29
Finally from eq. 3,
2%2B4%2Bc=9
highlight%28c=3%29
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highlight_green%28y=2x%5E2%2B4x%2B3%29