The standard form of a parabola is y=ax²+bx+c use the three given points to find the three unknown constants a, b, and c: -2=a+b+c............1 -2=4a+2b+c......... 2 -4=9a+3b+c...........3 equation 2 minus equation 1: 3a+b=0..........4 equation 3 minus equation 2: 5a+b=-2.........5 equation 5 minus equation 4: 2a=-2, so a=-1 plug a=-1 in equation 4: -3+b=0, so b=3 Plug a=-1, b=3 in equation 1: -2=-1+3+c, so c=-4 the parabola is y=-x²+3x-4
double check: when x=1, y=-1+3-4=-2 when x=2, y=-4+6-4=-2 when x=3, y=-9+9-4=-4 Yes.
