Find the minimum value of \(y = 3x^{2} - x - 6\).
Question 1 Report
Find the minimum value of \(y = 3x^{2} - x - 6\).
Answer Details
To find the minimum value of the quadratic function, we first need to find the vertex of the parabola. We can do this by using the formula:
\(-\frac{b}{2a}\)
where \(a\) is the coefficient of the squared term, and \(b\) is the coefficient of the linear term.
In this case, \(a = 3\) and \(b = -1\), so:
\(-\frac{b}{2a} = -\frac{-1}{2(3)} = \frac{1}{6}\)
This tells us that the vertex of the parabola occurs at \(x = \frac{1}{6}\). To find the minimum value of the function, we substitute this value of \(x\) into the function:
\(y = 3\left(\frac{1}{6}\right)^{2} - \frac{1}{6} - 6 = -6\frac{1}{12} = -\frac{25}{4}\)
Therefore, the minimum value of the function is \(-6\frac{1}{12}\), which is equivalent to \(-\frac{25}{4}\). So the answer is option B.
Download The App On Google Playstore
Everything you need to excel in your exams
Personalized AI Learning Chat Assistant
200,000+ Exam Questions Across IGCSE, JAMB, WAEC & NECO
Over 3,900 Lesson Notes
Offline Support - Learn Anytime, Anywhere
Green Bridge Timetable
Literature Summaries & Potential Questions
Track Your Performance & Progress
In-depth Explanations for Comprehensive Learning