Question 980271
(1,-2):{{{-2=a(1)^2+b(1)+c}}}
1.{{{a+b+c=-2}}}
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(-2,19):{{{-2=a(-2)^2+b(-2)+c}}}
2.{{{4a-2b+c=19}}}
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(3,4) : {{{4=a(3)^2+b(3)+c}}}
3.{{{9a+3b+c=4}}}
Subtract the first equation from second and third.
{{{4a-2b+c-a-b-c=19-(-2)}}}
{{{3a-3b=21}}}
4.{{{a-b=7}}}
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{{{9a+3b+c-a-b-c=4-(2)}}}
{{{8a+2b=6}}}
5.{{{4a+b=3}}}
Now add eq. 4 and eq. 5,
{{{a-b+4a+b=7+3}}}
{{{5a=10}}}
{{{a=2}}}
Then,
{{{2-b=7}}}
{{{-b=5}}}
{{{b=-5}}}
and,
{{{2-5+c=-2}}}
{{{c=1}}}
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{{{y=2x^2-5x+1}}}