SOLUTION: Find an equation in standard form of the parabola (-1,6), (1,4), (2,9)

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Question 671570: Find an equation in standard form of the parabola (-1,6), (1,4), (2,9)
Answer by MathLover1(20849) About Me  (Show Source):
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Find a quadratic function in standard form for each set of points.
(-1,6), (1,4), (2,9)

y=ax%5E2%2Bbx%2Bc
6=a%28-1%29%5E2%2Bb%28-1%29%2Bc ........ for (-1,6)
6=a-b%2Bc..........1
4=a%2B+b%2Bc ..........2............for (1,4)
9=4a%2B2b%2Bc .............3.........for (2,9)
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6=a-b%2Bc..........1
4=a%2B+b%2Bc ............for (1,4)..........2...add both 1 and 2
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10=2a%2B2c..........2a.........both sides divide by 2
5=a%2Bc......solve for a
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a=5-c.......substitute in 3
9=4%285-c%29%2B2b%2Bc
9=20-4c%2B2b%2Bc
9=20-3c%2B2b.....go to 2 and solve for b
4-a-c=b ..........2.......substitute a=5-c
4-%285-c%29-c=b
4-5%2Bc-c=b
highlight%28-1=b%29
now find c
9=20-3c%2B2%28-1%29
9=20-3c-2
9=18-3c
3c=18-9
3c=9
highlight%28c=3%29
now find a
a=5-c
a=5-3
highlight%28a=2%29
so, your equation is: y=2x%5E2-x%2B3