Find the equation of the axis of symmetry of the following parabola algebraically.

y, equals, x, squared, minus, 2, x, plus, 1
y=x
2
−2x+1

1 answer

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 \( x = 1 \).