Find the minimum value of \(y = 3x^{2} - x - 6\).
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Correct Answer: Option B
Explanation:
\(3x^{2} - x - 6 = y\)
\(a = 3, b = -1, c = -6\)
Minimum value of x = \(\frac{-b}{2a} = \frac{-(-1)}{6} = \frac{1}{6}\)
\(y(\frac{1}{6}) = 3(\frac{1}{6}^{2}) - \frac{1}{6} - 6 = -6\frac{1}{12}\)
\(3x^{2} - x - 6 = y\)
\(a = 3, b = -1, c = -6\)
Minimum value of x = \(\frac{-b}{2a} = \frac{-(-1)}{6} = \frac{1}{6}\)
\(y(\frac{1}{6}) = 3(\frac{1}{6}^{2}) - \frac{1}{6} - 6 = -6\frac{1}{12}\)