On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 4, negative 4), and goes through (negative 2, 0).

Question

The graph of the function f(x) = (x + 6)(x + 2) 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 function is increasing over (–∞, –4).
The function is negative over (–6, –2).

Answer 1

Let's analyze the information provided about the parabola in the coordinate plane.

1. The vertex is the maximum value.

   • False. Since the parabola opens upwards, the vertex represents the minimum value, not a maximum.

2. The axis of symmetry is x = –4.

   • True. The axis of symmetry of a parabola described by its vertex (h, k) is given by the line x = h. Since the vertex is at (-4, -4), the axis of symmetry is indeed x = -4.

3. The domain is all real numbers.

   • True. Parabolas are defined for all real numbers along the x-axis.

4. The function is increasing over (–∞, –4).

   • True. Since the vertex is at (-4, -4) and the parabola opens upward, the function will be decreasing from negative infinity up to x = -4 and then increasing for x > -4.

5. The function is negative over (–6, –2).

   • True. Because the parabola crosses the x-axis at (-6, 0) and (-2, 0), the section between these two points corresponds to negative y-values (the function is below the x-axis) when x is between -6 and -2.

Based on this analysis, the statements that apply are:

• The axis of symmetry is x = –4.
• The domain is all real numbers.
• The function is increasing over (–∞, –4).
• The function is negative over (–6, –2).

Final answer:

• True: The axis of symmetry is x = –4.
• True: The domain is all real numbers.
• True: The function is increasing over (–∞, –4).
• True: The function is negative over (–6, –2).
• False: The vertex is the maximum value.