the equation of a parabola is y = x² - 2x + 1. write the equation in vertex form. write any numbers as…

Explanation:

Step1: Recognize the form for completing the square

The general form of a quadratic function is $y = ax^{2}+bx + c$. Here $a = 1$, $b=-2$, $c = 1$. The vertex - form of a quadratic function is $y=a(x - h)^{2}+k$.

Step2: Complete the square

We have $y=x^{2}-2x + 1$. For the $x^{2}-2x$ part, using the formula $(m - n)^2=m^{2}-2mn + n^{2}$, where $m = x$ and $-2mn=-2x$, so $n = 1$. And $x^{2}-2x=(x - 1)^{2}-1$. Then $y=(x^{2}-2x)+1=((x - 1)^{2}-1)+1$.

Step3: Simplify the equation

$y=(x - 1)^{2}-1 + 1=(x - 1)^{2}$.

Answer:

$y=(x - 1)^{2}$