the equation of a parabola is y = x² - 8x + 16. write the equation in vertex form. write any numbers as…

Explanation:

Step1: Recognize perfect - square trinomial

The expression $x^{2}-8x + 16$ is in the form $a^{2}-2ab + b^{2}$ where $a=x$ and $b = 4$ since $2ab=2\times x\times4 = 8x$ and $b^{2}=16$. $y=x^{2}-8x + 16=(x - 4)^{2}$ The vertex - form of a parabola is $y=a(x - h)^{2}+k$, where $(h,k)$ is the vertex of the parabola. In the equation $y=(x - 4)^{2}$, we can rewrite it as $y=1(x - 4)^{2}+0$.

Answer:

$y=(x - 4)^{2}$