Advanced Math practice question

Answer: A. −2 < x < 4

f(x) = (x − 4)(x + 2), with zeros at −2 and 4. The parabola opens upward, so it is below the x-axis BETWEEN its zeros: −2 < x < 4. Check x = 0: f(0) = −8.

Why the other answers are wrong

B. x < −2 or x > 4

Outside the zeros the upward-opening parabola is positive, e.g. f(5) = 7.

C. x < 4

x < 4 includes x = −3, where f(−3) = 7 > 0.

D. −4 < x < 2

−4 < x < 2 has the zeros' signs reversed; f(−3) = 7, not negative.

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