Write the equation of a parabola in standard form that contains the points for (0,3), (1,2), (2,3)

Step-by-step explanation:

let the eq. of parabola be

y=ax²+bx+c

∵ (0,3),(1,2),(2,3) lie on it.

3=0+0+c

so c=3

and 2=1a+1b+c

2=a+b+3

a+b=-1

3=4a+2b+c

3=4a+2b+3

4a+2b=0

or 2a+b=0

b=-2a

substituting

a+(-2a)=-1

-a=-1

a=1

b=-2a=-2×1=-2

so eq. of parabola is

y=x²-2x+3

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