the equation of a parabola is y = x² - 6x + 9. write the equation in vertex form. write any numbers as…

Explanation:

Step1: Recognize the perfect - square trinomial

The given equation $y=x^{2}-6x + 9$ is in the form of $a^{2}-2ab + b^{2}$ where $a = x$ and $b = 3$ since $-6x=-2\times x\times3$ and $9 = 3^{2}$.

Step2: Factor the trinomial

Using the formula $a^{2}-2ab + b^{2}=(a - b)^{2}$, we can factor $x^{2}-6x + 9$ as $(x - 3)^{2}$.

Answer:

$y=(x - 3)^{2}$