Let a, b, and c be fixed numbers with a 0 and let f(x) = $a x ^ { 2 }$ + bx + c. Which of the following properties is true of the graph of f(x) ?
A) f(x) is always concave up
B) f(x) has either a relative maximum or inflection point
C) f(x) has one relative maximum
D) f(x) has one inflection point
E) none of these

Question

Let a, b, and c be fixed numbers with a > 0 and let f(x) = $a x ^ { 2 }$ + bx + c. Which of the following properties is true of the graph of f(x) ?
A) f(x) is always concave up
B) f(x) has either a relative maximum or inflection point
C) f(x) has one relative maximum
D) f(x) has one inflection point
E) none of these

Quizplus · Accepted Answer

The graph of $f(x) = ax^2 + bx + c$ is a parabola, and since $a > 0$, it opens upwards, making it always concave up.

Let A, B, and C Be Fixed Numbers with a >