83359
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Quadratic Functions: Factored Form

Question 83359 • *Integrated Math II Full

The graph of the function f(x) = (x + 6)(x + 2) is shown. Which statements describe the graph? Check all that apply.

Answer
A
The vertex is the maximum value.
B
The axis of symmetry is x = –4.
C
The domain is all real numbers.
D
The function is increasing over (–∞, –4).
E
The function is negative over (–6, –2).

Explanation

The zeros are x = −6 and x = −2, so the axis of symmetry is halfway between them: x = (−6 + −2)/2 = −4. The parabola opens upward, so its vertex is a minimum, not a maximum, and the function decreases before x = −4. A polynomial is defined for every real x, and because the graph opens upward and crosses the x-axis at −6 and −2, it is negative between those roots.

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