Chapter 9 - Section 9.1 - Solving Systems of Linear Equations in Three Variables and Problem Solving - Exercise Set - Page 642: 62

$(1,-2, 3)$

$y=ax^2+bx+c$ $(-1,6)$, $(1,2)$, $(2,3)$ $x=-1$ $y=ax^2+bx+c$ $y=a(-1)^2+b*-1+c$ $6=a-b+c$ $x=1$ $y=ax^2+bx+c$ $2=a*1^2+b*1+c$ $2=a+b+c$ $x=2$ $y=ax^2+bx+c$ $3=a*2^2+b*2+c$ $3=4a+2b+c$ $6=a-b+c$ $2=a+b+c$ $3=4a+2b+c$ $a+b+c+a-b+c=6+2$ $2a+2c=8$ $2(a+c=4)$ $a+c=4$ $4a+2b+c+2(a-b+c)=3+2*6$ $4a+2b+c+2a-2b+2c=3+12$ $6a+3c=15$ $3(2a+c=5)$ $2a+c=5$ $2a+c=5$ $a+c=4$ $2a+c-(a+c)=5-4$ $2a+c-a-c=1$ $a=1$ $a+c=4$ $1+c=4$ $c=3$ $a+b+c=2$ $1+b+3=2$ $4+b=2$ $b=-2$