First, the graph is a parbole, this is a square function, so it can not be the option a) because it is a linear function.
Second, the vertix of the parabole is the point (0,3), so use the general vertex form of the parabole:
y = A(x - h)^2 + k, where h and k represent the vertex (h,k).
So, the form of the funtion is y = A (x-0)^2 - 3 = Ax^2 - 3
Now, you also know that the roots of the parabole are close to -1 and 1 but they are not those exact value.
So, find the roots for any of the possible options:
b) f(x) = 2x^2 - 3 = 0 => 2x^2 = 3 => x^2 = 3/2 => x = +/- √(3/2) ≈ +/- 1.22
That is a very plausible answer
c) f(x) = (1/2)x^2 - 3 = 0 => x^2 = 2*3 = 6 => x = +/- √6 ≈ +/- 2.45, which is very far from the roots shown on the graph.
3) f(x) = x^2 - 3 = 0 => x^2 = 3 => x = +/- √3 ≈ +/- 1.73, which is not so close to +/- 1.
So, the answer is the option b) f(x) = 2x^2 - 3
