10
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Quadratic Functions: Standard Form

Question 10 • FL-1200700-Mathematics for College Algebra MIS

The graph of the function f(x) = x2 + 8x + 12 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 range is all real numbers.
E
The function is increasing over (–∞, –4).
F
The x-intercepts are at (–6, 0) and (–2, 0).

Explanation

The parabola opens upward because the coefficient of x² is positive, so its vertex is a minimum, not a maximum. Its axis of symmetry is x = −8 ÷ 2 = −4, and a quadratic function has a domain of all real numbers. Factoring gives x² + 8x + 12 = (x + 6)(x + 2), so the x-intercepts are (−6, 0) and (−2, 0).

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