SOLUTION: Find the values of a,b,and c such that the parabola y=ax^2+bx+c contains the points (-3,3),(-1,5)and (3,33).

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Question 441899: Find the values of a,b,and c such that the parabola y=ax^2+bx+c contains the points (-3,3),(-1,5)and (3,33).
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Plugging the coordinates of the points into y=ax%5E2%2Bbx%2Bc, we get the system:
system%283=9a-3b%2Bc%2C+-1=25a%2B5b%2Bc%2C+33=9a%2B3b%2Bc%29. Subtracting first equation from
the third we get:30=6b => b=5.Isolate c from the first and second
equation:c=3-9a+3b and c=-1-25a-5b, from these two equalities we get:
3-9a+3b=-1-25a-5b simplifying this equality we get:4a+2b=-1, substituting b=5,
we have: 4a+2*5=-1 => a=-11/4. Substituting a and b we find c:
c=3+99/4+15 => c=171/4.
You can solve the system using Cramer's Rule.
Done.