find the minimum value of the parabola y = x² - x. simplify your answer and write it as a proper fraction…

Answer:

$-\frac{1}{4}$

Explanation:

Step1: Rewrite in vertex - form

$y=x^{2}-x=(x - \frac{1}{2})^{2}-\frac{1}{4}$

Step2: Identify the minimum value

For a parabola $y=a(x - h)^{2}+k$ with $a>0$, the vertex is $(h,k)$. Here $a = 1>0$, $h=\frac{1}{2}$, $k =-\frac{1}{4}$. The minimum value of the parabola is $k=-\frac{1}{4}$.