Question

The graph of a function f(x)
passes through the following points: ( 0,2), (1,0),(-1,0)


Which of the following could be f(x)
?

Answer 1

If f has zeros at x = 1 and x = −1, a simple polynomial form is f(x) = a(x−1)(x+1) = a(x^2−1). Use (0,2):

2 = a(0^2 − 1) = −a → a = −2.

So one possible f is f(x) = −2(x^2 − 1) = −2x^2 + 2.