Question

Which function is negative for the interval [–1, 1]?

On a coordinate plane, a curved line with a minimum value of (negative 1, negative 2), crosses the x-axis at (negative 2.5, 0) and (0.5, 0), and the y-axis at (0, negative 1).

On a coordinate plane, a curved line with a minimum value of (0, negative 2), crosses the x-axis at (negative 1.5, 0) and (1.5, 0).

On a coordinate plane, a curved line with a maximum value of (0, 2) and a minimum value of (1.5, negative 2.75), crosses the x-axis at (negative 0.6, 0) and (0.6, 0).

On a coordinate plane, a curved line with a maximum value of (negative 1.25, 4) and a minimum value of (1.5, negative 3.5), crosses the x-axis at (negative 1.75, 0), (0.75, 0), and (1.75, 0), and crosses the y-axis at (0, 2).

Answer 1

The second graph — the curve with vertex (0, −2) and x‑intercepts at (−1.5, 0) and (1.5, 0).

Reason: its roots are at x = ±1.5, so for every x with |x| ≤ 1 (< 1.5) the curve lies between the roots and therefore y < 0.