Question 342559
The general quadratic equation is {{{y=ax^2+bx+c}}}
Use the three points to get three equations in a,b, and c.
(-1,-1):{{{-1=a(-1)^2+b(-1)+c}}}
1.{{{a-b+c=-1}}}
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(1,-3):{{{-3=a(1)^2+b(1)+c}}}
2.{{{a+b+c=-3}}}
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(2,8):{{{8=a(2)^2+b(2)+c}}}
3.{{{4a+2b+c=8}}}
Add eq. 1 and eq. 2,
{{{a-b+c+a+b+c=-1-3}}}
{{{2a+2c=-4}}}
4.{{{a+c=-2}}}
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Double eq. 1 and add to eq. 3,
{{{2a-2b+2c+4a+2b+c=-2+8}}}
{{{6a+3c=6}}}
5.{{{2a+c=2}}}
Subtract eq. 4 from eq. 5,
{{{2a+c-a-c=2-(-2)}}}
{{{highlight(a=4)}}}
Then work backwards,
{{{a+c=-2}}}
{{{4+c=-2}}}
{{{highlight(c=-6)}}}
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{{{a+b+c=-3}}}
{{{4+b-6=-3}}}
{{{highlight(b=-1)}}}
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{{{highlight_green(y=4x^2-x-6)}}}
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Verify the solution by plugging the x values into the equation and comparing the y values.