To determine the line of symmetry for a quadratic function with a given vertex, let's recall the general properties of a quadratic function.
The standard form of a quadratic function is:
[tex]\[ y = ax^2 + bx + c \][/tex]
However, the vertex form of a quadratic function, which is more useful for our purposes, is given by:
[tex]\[ y = a(x - h)^2 + k \][/tex]
where [tex]\( (h, k) \)[/tex] is the vertex of the quadratic function.
The line of symmetry (also known as the axis of symmetry) for a quadratic function in vertex form is a vertical line that passes through the vertex. This line is given by the equation:
[tex]\[ x = h \][/tex]
Given the vertex of the quadratic function is [tex]\( (2, 3) \)[/tex]:
- [tex]\( h = 2 \)[/tex]
- [tex]\( k = 3 \)[/tex]
So, the equation for the line of symmetry will be:
[tex]\[ x = 2 \][/tex]
Therefore, the correct answer to the question is:
[tex]\[ x = 2 \][/tex]
