Question 950291
Use the quadratic equation,
{{{y=fx^2+gx+h}}}
Now input each point to get an equation,
{{{0=f(0)+g(0)+h}}}
{{{h=0}}}
So now the final two equations only will have f and g.
{{{1=f(1)+g(1)}}}
1.{{{f+g=1}}}
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{{{8=f(4)+g(2)}}}
{{{4f+2g=8}}}
2.{{{2f+g=4}}}
Subtract eq. 1 from eq. 2,
{{{2f+g-f-g=4-1}}}
{{{f=3}}}
So then,
{{{3+g=1}}}
{{{g=-2}}}
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{{{y=3x^2-2x}}}
{{{y=x(3x-2)}}}