Question 1206103
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Plug each (x,y) pair into the general form of the equation to get three equations in a, b, and c; then solve that system of equations.<br>
(-1,0): {{{a-b+c=0}}} [1]<br>
(2,-54): {{{4a+2b+c=-54}}} [2]<br>
(5,-252): {{{25a+5b+c=-252}}} [3]<br>
Eliminate c between [1] and [2], and between [2] and [3], to get two equations in a and b.<br>
[2]-[1]: {{{3a+3b=-54}}} [4]<br>
[3]-[2]: {{{21a+3b=-198}}} [5]<br>
Eliminate b between [4] and [5] and solve for a.<br>
[5]-[4]: {{{18a=-144}}}<br>
{{{a=-144/18=-8}}}<br>
Substitute a=-8 in [4] and solve for b:
{{{-24+3b=-54}}}
{{{3b=-30}}}
{{{b=-10}}}<br>
Substitute a=-8 and b=-10 in [1] and solve for c:
{{{-8+10+c=0}}}
{{{c=-2}}}<br>
ANSWER: {{{y=-8x^2-10x-2}}}<br>
Simplified....<br>
{{{y=-2(4x^2+5x+1)}}}
{{{y=-2(x+1)(4x+1)}}}<br>
CHECK:
{{{f(-1)=(-2)(0)(-3)=0}}}
{{{f(2)=(-2)(3)(9)=-54}}}
{{{f(5)=(-2)(6)(21)=-252}}}<br>