Question 1007156
Use the points to get three equation in a,b, and c.
{{{9=a(2)^2+b(2)+c}}}
1.{{{4a+2b+c=9}}}
{{{13=a(-2)^2+b(-2)+c}}}
2.{{{4a-2b+c=13}}}
{{{-2=a(1)^2+b(1)+c}}}
3.{{{a+b+c=-2}}}
Subtract eq. 3 from eq. 1 and 2.
{{{4a+2b+c-a-b-c=9-(-2)}}}
4.{{{3a+b=11}}}
and
{{{4a-2b+c-a-b-c=13-(-2)}}}
{{{3a-3b=15}}}
5.{{{a-b=5}}}
Adding eq. 4 and 5,
{{{3a+b+a-b=11+5}}}
{{{4a=16}}}
{{{a=4}}}
Then working backwards,
5.{{{a-b=5}}}
{{{4-b=5}}}
{{{b=-1}}}
and finally,
3.{{{a+b+c=-2}}}
{{{4-1+c=-2}}}
{{{c=-5}}}
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{{{highlight_green(y=4x^2-x-5)}}}
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*[illustration Dss7.JPG].