To find the equation of the axis of symmetry of the parabola represented by the equation \( y = x^2 - 2x + 1 \), we can use the formula for the axis of symmetry of a quadratic function of the form \( y = ax^2 + bx + c \). The formula for the axis of symmetry is given by:
\[ x = -\frac{b}{2a} \]
In this case, from the equation \( y = x^2 - 2x + 1 \):
- \( a = 1 \)
- \( b = -2 \)
- \( c = 1 \)
Now, we substitute \( a \) and \( b \) into the formula:
\[ x = -\frac{-2}{2 \cdot 1} = \frac{2}{2} = 1 \]
Thus, the axis of symmetry is given by the equation:
\[ x = 1 \]
This means that the parabola is symmetric about the vertical line \( x = 1 \).
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