Analyze the Parabola y=(x-2)(x+1): Finding the Turning Point

To determine if the function $y = (x-2)(x+1)$ has a minimum or maximum point, we start by converting it from product form to standard form:

$y = (x-2)(x+1)$

Expanding the expression:

$y = x^2 + x - 2x - 2$

Simplify:

$y = x^2 - x - 2$

In standard form, $y = x^2 - x - 2$, the coefficient of $x^2$, which is $a = 1$, is positive. A positive $a$ indicates the parabola opens upwards.

Since the parabola opens upwards, it has a minimal point (vertex) as its lowest point.

Therefore, the parabola $y = (x-2)(x+1)$ has a minimal point.