Question 338743
The general quadratic equation is {{{y=ax^2+bx+c}}}
Substitute your three points to get three equations in a,b, and c.
(-1,0):{{{0=a(-1)^2+b(-1)+c}}}
1.{{{a-b+c=0}}}
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(0,1):{{{1=a(0)^2+b(0)+c}}}
2.{{{c=1}}}
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(2,21):{{{21=a(2)^2+b(2)+c}}}
3.{{{4a+2b+c=21}}}
Substitute eq. 2 into eq.1 and eq. 3,
{{{a-b+1=0}}}
4.{{{a-b=-1}}}
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{{{4a+2b+1=21}}}
{{{4a+2b=20}}}
5.{{{2a+b=10}}}
Add eq. 4 and eq. 5,
{{{a-b+2a+b=9}}}
{{{3a=9}}}
{{{a=3}}}
Then from eq. 4,
{{{3-b=-1}}}
{{{b=4}}}
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{{{highlight(y=3x^2+4x+1)}}}