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

Question

Does the parable

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

Is there a minimum or maximum point?

00:00 Does the parabola have a maximum or minimum point?

00:03 Let's properly open parentheses, multiply each factor by each factor

00:13 Let's group the factors

00:21 The coefficient A of the function is positive, therefore the parabola is smiling

00:26 Therefore the parabola has a minimum point

00:31 And this is the solution to the question

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.

Minimal point