Question

Which is the graph of f(x) = –(x + 3)(x + 1)?

On a coordinate plane, a parabola opens down. It goes through (0, negative 3), has a vertex at (2, 1), and goes through (4, negative 3).

On a coordinate plane, a parabola opens down. It goes through (negative 3, 0), has a vertex at (negative 2, 1), and goes through (negative 1, 0).

On a coordinate plane, a parabola opens up. It goes through (negative 4, 3), has a vertex at (negative 2, negative 1), and goes through (0, 3).

Answer 1

f(x) = −(x+3)(x+1) = −x^2 − 4x − 3. So:
- Zeros at x = −3 and x = −1 → points (−3,0) and (−1,0).
- Vertex at x = −b/(2a) = −(−4)/(2·−1) = −2, and f(−2)=1 → vertex (−2,1).
- Opens down (a = −1) and y-intercept f(0)=−3 → (0,−3).

The second graph (opens down, through (−3,0), vertex (−2,1), through (−1,0)) is the correct one.