Find the minimum value of the parabola \( y=x^{2}+6 x \). Simplify your answer and write it as a proper fraction, improper fraction, or integer.

To find the minimum value of the parabola given by the equation \( y = x^2 + 6x \), we can complete the square. First, we can rewrite the quadratic expression: \[ y = x^2 + 6x \] Next, we complete the square: \[ y = (x^2 + 6x + 9) - 9 \] This simplifies to: \[ y = (x + 3)^2 - 9 \] The expression \((x + 3)^2\) represents a parabola that opens upwards and is always non-negative. The minimum value occurs when \((x + 3)^2 = 0\), which happens when \(x = -3\). By plugging \(x = -3\) back into the equation, we find the minimum value: \[ y = (0) - 9 = -9 \] Thus, the minimum value of the parabola \(y = x^2 + 6x\) is \[ \boxed{-9}. \]