Let's analyze the quadratic function given by \(\( x = 144 \)\).
### Step-by-Step Solution
1. Identify the Form of the Equation:
The equation \(\( x = 144 \)\) represents a vertical line at \(\( x = 144 \)\) in the Cartesian coordinate system.
2. Axis of Symmetry:
For a vertical line like \(\( x = 144 \)\), the axis of symmetry is the line itself. This is because a vertical line is symmetrically positioned along itself.
- Therefore, the axis of symmetry is \(\( x = 144 \)\).
3. Vertex:
The concept of a vertex is typically used for parabolic functions in the form \(\( y = ax^2 + bx + c \)\). However, in this case, since the graph is a vertical line, it does not have a single point of extremity (like a minimum or maximum point in parabolas) in the traditional \(\( (x, y) \)\) sense.
- Instead, we consider the “vertex” of the vertical line \(\( x = 144 \)\) as extending infinitely along the y-axis at \(\( x = 144 \)\).
- Hence, we can represent the vertex in terms of coordinates as \(\( (144, \infty) \)\).
### Summary
- Axis of Symmetry: \(\( x = 144 \)\)
- Vertex: \(\( (144, \infty) \)\)
Therefore, the axis of symmetry and the vertex for the quadratic function \(\( x = 144 \)\) are \(\( x = 144 \)\) and \(\( (144, \infty) \)\), respectively.
