Question

The graph of the function f(x) = x2 + 8x + 12 is shown. Which statements describe the graph? Check all that apply.

The vertex is the maximum value.
The axis of symmetry is x = –4.
The domain is all real numbers.
The range is all real numbers.
The function is increasing over (–∞, –4).
The x-intercepts are at (–6, 0) and (–2, 0).

Answer 1

True:
- The axis of symmetry is x = –4. (Vertex at x = -b/(2a) = -8/2 = -4.)
- The domain is all real numbers. (Quadratic defined for all x.)
- The x-intercepts are at (–6, 0) and (–2, 0). (x^2+8x+12=(x+6)(x+2).)

False:
- The vertex is the maximum value. (The vertex (-4, -4) is a minimum since the parabola opens upward.)
- The range is all real numbers. (Range is y ≥ -4.)
- The function is increasing over (–∞, –4). (It is decreasing on (–∞, –4) and increasing on (–4, ∞).)