Question

Which quadratic equation fits the data in the table?

Answer 1

`y=x^2-4x+1`

First option is correct.

Explanation:

From the given table, we take three points (0,1), (1,-2) and (2,-3)

Now, let the quadratic equation is
`y=ax^2+bx+c`

Use the first point (0,1)

`1=a(0)^2+b(0)+c\\\\c=1`

Thus, the equation becomes
`y=ax^2+bx+1`

Now, use the point (1,-2)

`-2=a(1)^2+b(1)+1\\\\a+b+1=-2\\\\a+b=-3...(i)`

Now, use the point (2,-3)

`-3=a(2)^2+b(2)+1\\\\4a+2b+1=-3\\\\4a+2b=-4\\\\2a+b=-2...(ii)`

Subtract (i) and (ii)

a-2a= -3+2

-a = -1

a = 1

Now, substituting this value in (i)

1 + b = -3

b = -3-1

b = -4

Therefore, the quadratic equation is
`y=x^2-4x+1`

First option is correct.