Advanced MathMediumMinimum value of a quadratic with a leading coefficient
Advanced Math practice question
The function f is defined by f(x) = 3x² + 12x − 1. What is the minimum value of f(x)?
Answer: -13 or −13
The vertex is at x = −12/(2 · 3) = −2. There, f(−2) = 3(4) − 24 − 1 = −13, the minimum since the parabola opens upward.
Common wrong answers
- If you answered -2
- −2 is the x-coordinate of the vertex, not the minimum VALUE of f.
- If you answered -1
- −1 is f(0), the y-intercept, not the lowest point.
- If you answered -37
- −37 comes from 3(4) − 48 − 1, doubling the 12x term; 12(−2) = −24.
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