Question

For all functions of the form f(x) = ax2 + bx + c, which is true when b = 0?

The graph will always have zero x-intercepts.
The function will always have a minimum.
The y-intercept will always be the vertex.
The axis of symmetry will always be positive.

Answer 1

Correct choice: "The y-intercept will always be the vertex."

Reason: If b = 0 then f(x) = ax^2 + c. The axis of symmetry is x = −b/(2a) = 0, so the vertex is at x = 0 and its y-value is f(0) = c — the y‑intercept.

Quick refutations of the others:
- Not always zero x‑intercepts: ax^2 + c = 0 can have 0, 1, or 2 real solutions depending on the sign/values of a and c.
- Not always a minimum: if a > 0 it's a minimum, if a < 0 it's a maximum.
- Axis of symmetry is x = 0, which is not positive.