At what value of x is the function x\(^2\) + x + 1 minimum?

  • A -1
  • B \(-\frac{1}{2}\)
  • C \(\frac{1}{2}\)
  • D 1
jamb 1990mathematics

The correct answer is B. \(-\frac{1}{2}\)

The function \(x^2 + x + 1\) is a quadratic function, and its graph is a parabola. 

The minimum value of the function occurs at the vertex of the parabola. 

The x-coordinate of the vertex of a parabola represented by the quadratic function \(ax^2 + bx + c\) is given by the formula \(x = -\frac{b}{2a}\). 

In this case, \(a = 1\) and \(b = 1\), so the x-coordinate of the vertex is \(x = -\frac{1}{2}\).

Therefore, the minimum value of the function \(x^2 + x + 1\) occurs at \(x = -\frac{1}{2}\).

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