Answer
$a=3$
$b=4$
$c=-1$
Work Step by Step
Given Equation,
$y=ax^{2}+bx+c$
Given ordered pair solutions
$(1,6), (-1,-2),(0,-1)$
Substituting each ordered pair solution into the equation,
$y=ax^{2}+bx+c$
$6=a(1)^{2}+b(1)+c$
$a+b+c=6$ Equation $(1)$
$y=ax^{2}+bx+c$
$-2=a(-1)^{2}+b(-1)+c$
$a-b+c=-2$ Equation $(2)$
$y=ax^{2}+bx+c$
$-1=a(0)^{2}+b(0)+c$
$c=-1$
Subtracting Equation $(2)$ From Equation $(1)$
$a+b+c-(a-b+c)=6-(-2)$
$a+b+c-a+b-c=6+2$
$2b = 8$
$b=4$
Substituting $b$ and $c$ values in Equation $(1)$
$a+b+c=6$
$a+4-1=6$
$a+3=6$
$a=6-3$
$a= 3$
