Find the axis of symmetry of the curve \(y = x^{2} - 4x - 12\).
Answer Details
To find the axis of symmetry of a quadratic equation in the form of \(y = ax^2 + bx + c\), we need to use the formula:
$$x = \frac{-b}{2a}$$
Comparing the given equation \(y = x^2 - 4x - 12\) with the standard form of the quadratic equation, we have:
$$a = 1, b = -4, c = -12$$
Substituting the values in the formula, we get:
$$x = \frac{-(-4)}{2(1)} = 2$$
Therefore, the axis of symmetry of the curve is the vertical line passing through the point \((2,0)\) and the equation of this line is:
$$x = 2$$
Hence, the correct answer is "x = 2".