The given equation of the parabola is \( y = x^2 + 9 \).
This is a standard form of a quadratic equation \( y = ax^2 + bx + c \), where:
- \( a = 1 \)
- \( b = 0 \)
- \( c = 9 \)
Since \( a > 0 \), the parabola opens upward. The minimum value of the parabola occurs at its vertex.
The x-coordinate of the vertex can be found using the formula: \[ x = -\frac{b}{2a} \] Substituting \( a \) and \( b \): \[ x = -\frac{0}{2 \cdot 1} = 0 \]
Now, substitute \( x = 0 \) back into the equation to find the corresponding \( y \)-value: \[ y = (0)^2 + 9 = 9 \]
Thus, the minimum value of the parabola \( y = x^2 + 9 \) is: \[ \boxed{9} \]