Answer:
![f(x)=x^2-x+2](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2-x%2B2)
Step-by-step explanation:
Quadratic equation form :
--1
We are given points :(-1,4), (0,2) and (2,4).
Substitute the point (0,2) in the quadratic equation.
![2=a(0)^2+b(0)+c](https://tex.z-dn.net/?f=2%3Da%280%29%5E2%2Bb%280%29%2Bc)
![2=c](https://tex.z-dn.net/?f=2%3Dc)
Thus the value of c is 2
Substitute the value of c in 1
Thus equation becomes:
--2
Now substitute the point (-1,4) in 2
---3
Now substitute point (2,4) in 2
--4
Now solve 3 and 4 to find the value of a and b
Substitute the value of a from 3 in 4
Substitute the value of b in 3
Thus a = 1, b =-1 and c = 2
Substitute the values in 1
![y=x^2-x+2](https://tex.z-dn.net/?f=y%3Dx%5E2-x%2B2)
Thus the quadratic function that contains the points (-1,4), (0,2) and (2,4) is ![f(x)=y=x^2-x+2](https://tex.z-dn.net/?f=f%28x%29%3Dy%3Dx%5E2-x%2B2)
Hence Option 3 is correct.