Question

The a value of a function in the form f(x) = ax2 + bx + c is negative. Which statement must be true?

The vertex is a maximum.
The y-intercept is negative.
The x-intercepts are negative.
The axis of symmetry is to the left of zero.

Answer 1

Answer: The vertex is a maximum.

Reason: If a < 0 the parabola opens downward, so the vertex is the highest point.

Counterexamples to the other statements:
- y-intercept is negative? No — y-intercept = c, can be positive (e.g. f(x) = -x^2 + 1 has c = 1).
- x-intercepts are negative? No — roots depend on b and c (e.g. f(x) = -x^2 - 1 has no real roots; f(x) = -x^2 + 1 has roots ±1).
- axis of symmetry is left of zero? No — axis x = -b/(2a) can be positive (e.g. f(x) = -x^2 + 4x has axis at x = 2).