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

Question

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

Answer 1

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 $y=a{x}^2+bx+c$. 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 $x=1$.