Answer :
Let's analyze the quadratic function given by [tex]\( x = 144 \)[/tex].
### Step-by-Step Solution
1. Identify the Form of the Equation:
The equation [tex]\( x = 144 \)[/tex] represents a vertical line at [tex]\( x = 144 \)[/tex] in the Cartesian coordinate system.
2. Axis of Symmetry:
For a vertical line like [tex]\( x = 144 \)[/tex], 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 [tex]\( x = 144 \)[/tex].
3. Vertex:
The concept of a vertex is typically used for parabolic functions in the form [tex]\( y = ax^2 + bx + c \)[/tex]. 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 [tex]\( (x, y) \)[/tex] sense.
- Instead, we consider the “vertex” of the vertical line [tex]\( x = 144 \)[/tex] as extending infinitely along the y-axis at [tex]\( x = 144 \)[/tex].
- Hence, we can represent the vertex in terms of coordinates as [tex]\( (144, \infty) \)[/tex].
### Summary
- Axis of Symmetry: [tex]\( x = 144 \)[/tex]
- Vertex: [tex]\( (144, \infty) \)[/tex]
Therefore, the axis of symmetry and the vertex for the quadratic function [tex]\( x = 144 \)[/tex] are [tex]\( x = 144 \)[/tex] and [tex]\( (144, \infty) \)[/tex], respectively.
### Step-by-Step Solution
1. Identify the Form of the Equation:
The equation [tex]\( x = 144 \)[/tex] represents a vertical line at [tex]\( x = 144 \)[/tex] in the Cartesian coordinate system.
2. Axis of Symmetry:
For a vertical line like [tex]\( x = 144 \)[/tex], 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 [tex]\( x = 144 \)[/tex].
3. Vertex:
The concept of a vertex is typically used for parabolic functions in the form [tex]\( y = ax^2 + bx + c \)[/tex]. 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 [tex]\( (x, y) \)[/tex] sense.
- Instead, we consider the “vertex” of the vertical line [tex]\( x = 144 \)[/tex] as extending infinitely along the y-axis at [tex]\( x = 144 \)[/tex].
- Hence, we can represent the vertex in terms of coordinates as [tex]\( (144, \infty) \)[/tex].
### Summary
- Axis of Symmetry: [tex]\( x = 144 \)[/tex]
- Vertex: [tex]\( (144, \infty) \)[/tex]
Therefore, the axis of symmetry and the vertex for the quadratic function [tex]\( x = 144 \)[/tex] are [tex]\( x = 144 \)[/tex] and [tex]\( (144, \infty) \)[/tex], respectively.
