Uncovering the Vertex: Analyzing y = (x+1)(-x-1) for Extremes

Question

Does the parable

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

Is there a minimum or maximum point?

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

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

00:12 Let's collect terms

00:21 The coefficient A of the function is negative, therefore the parabola is sad

00:25 Therefore the parabola has a maximum point

00:31 And this is the solution to the question

To solve this problem, follow these steps:

Step 1: Expand the quadratic function:

The given function is $y = (x+1)(-x-1)$ .

Expanding this, we have:

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

Step 2: Determine the nature using the leading coefficient:

The quadratic function is $y = -x^2 - 2x - 1$ .

Here, the leading coefficient $a = -1$ . Since the leading coefficient is negative, the parabola opens downwards.

Therefore, the quadratic function has a highest point, or a maximum.

Thus, the solution to the problem is that the quadratic function has a highest point.

Highest point