Question 318422
The general equation for a parabola is,
{{{y=ax^2+bx+c}}}
1.(-2,3):{{{3=4a-2b+c}}}
2.(-1,1):{{{1= a - b + c}}}
3.(1,9):{{{9= a + b + c }}}
Solve for a,b,c using elimination, substitution, or matrix methods.
Solve for b by subtracting eq. 2 and eq. 3,
{{{a-b+c-a-b-c=1-9}}}
{{{-2b=-8}}}
{{{highlight(b=4)}}}
Then substituting for b, subtract eq. 3 from eq. 1,
{{{4a - 8 + c - a - 4 - c=3 - 9}}}
{{{3a-12=-6}}}
{{{3a=6}}}
{{{highlight(a=2)}}}
Finally from eq. 3,
{{{2+4+c=9}}}
{{{highlight(c=3)}}}
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{{{highlight_green(y=2x^2+4x+3)}}}