Answer:

y= x²-3x+6

Step-by-step explanation:

let y= ax²+bx+c

we need 3 coordinates to substitute (0,6) (1,4) (2,4)

6=a×0²+b×0+c

c=6

4=a×1²+b×1+6

a+b+6=4

a+b= -2 (transpose)

4=a×2²+b×2+6

4a+2b+6=4

4a+2b= -2 (transpose)

2a+b= -1 (divide by 2 to make it easier)

solve the slant equations

2a-a + b-b = -1 - (-2)

a = -1 +2 = 1

substitute a to a slant equation:

1 + b = -2

b = -3 (transpose)

go back to original equation. substitute the values of a,b,c

y= 1×x²-3x+6

y=x²-3x+6

hope this helps