Identify the quadratic function that contains the points (-1,1), (0,-2) and (2,4).identify the quadratic function that contains the points (-1,1), (0,-2) and (2,4).

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