y=ax²+bx+c
(x,y)
(-1,1)
(0,-2)
(2,4)
sub them and solve
(-1,1)
1=a(-1)²+b(-1)+c
1=a-b+c
(0,-2)
0=a(-2)²+b(-2)+c
0=4a-2b+c
(2,4)
4=a(4)²+b(2)+c
4=4a+2b+c
now we got
1=a-b+c
0=4a-2b+c
4=4a+2b+c
we can eliminate the c's from all equations
multiply first equation by -1 and add to 2nd equation then 3rd to cancel c's
-1=-a+b-c
0=4a-2b+c +
-1=3a-b
-1=a+b-c
4=4a+2b+c +
3=5a+3b
1=a-b+c
-1=3a-b
3=5a+3b
eliminate b's
multiply 2nd eqyat by 3 and add to 3rd
-3=9a-3b
3=5a+3b +
0=14a
a=0
sub back
3=5(0)+3b
3=3b
1=b
sub back
1=a-b+c
1=0-1+c
1=-1+c
add 1
2=c
the equation is
y=0x²+1x+2 or
y=x+2
