Find an equation in standard form of the parabola passing through the points

Question

(0,0), (1,-2), (-1,-4)

Answer 1

y=ax^2+bx+c

(0,0)

0=c

(1,-2)

-2=a+b+c

(-1,-4)

-4=a-b+c

substitute c=0

-2=a+b

-4=a-b

add

-6=2a

a=-3

-2=-3+b

b=1

y=-3x^2+x is the equation