Question 1080078
First use the point of one of the given roots,  (0,2).

{{{y=a*0^2+b*0+c}}}
{{{2=0+0+c}}}
{{{highlight(c=2)}}}


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Make two equations with each of the other given points.
{{{ax^2+bx=y-c}}}
{{{ax^2+bx=y-2}}}
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{{{a*(-1)^2+b*(-1)=5-2}}}
{{{a-b=3}}}
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{{{a*3^2+b*3=8-2}}}
{{{9a+3b=6}}}, simplifiable,
{{{3a+b=2}}}
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Now solve this system:  {{{system(a-b=3,2a+b=2)}}}
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