To determine the axis of symmetry of the function [tex]\( f(x) = (x-1)^2 + 2 \)[/tex], follow these steps:
1. Identify the general form of the given quadratic function. The function provided, [tex]\( f(x) = (x-1)^2 + 2 \)[/tex], is already in the vertex form. The vertex form of a quadratic function is expressed as:
[tex]\[
f(x) = (x-h)^2 + k
\][/tex]
where [tex]\((h, k)\)[/tex] is the vertex of the parabola.
2. Based on the vertex form [tex]\( (x-h)^2 + k \)[/tex]:
- [tex]\( h = 1 \)[/tex]
- [tex]\( k = 2 \)[/tex]
3. The axis of symmetry for a parabola in this form is a vertical line that passes through the vertex of the parabola. The equation for the axis of symmetry is given by [tex]\( x = h \)[/tex], where [tex]\( h \)[/tex] is the x-coordinate of the vertex.
4. Given the vertex [tex]\((h, k) = (1, 2)\)[/tex], the axis of symmetry is the vertical line that passes through [tex]\( x = 1 \)[/tex].
Therefore, the axis of symmetry for the function [tex]\( f(x) = (x-1)^2 + 2 \)[/tex] is:
[tex]\[ x = 1 \][/tex]
