If fx ax2 bx c what can you say about the values of a b

Question

Question: (a) If f(x) = ax² + bx + c, what can you say about the values of a, b, and c if:

(i) (1, 1) is on the graph of f(x)?

(ii) (1, 1) is the vertex of the graph of f(x)? [Hint: The axis of symmetry is x = -b/(2a).]

(iii) The y-intercept of the graph is (0, 6)?

(b) Find a quadratic function satisfying all three conditions.