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?

00:08 Does the parabola have a highest or lowest point?

00:11 Alright, first let's expand the parentheses by multiplying each factor together.

00:20 Next, let's gather all the like terms. This will simplify our expression.

00:29 Since the coefficient, A, is negative, the parabola opens downward. Think of it as a sad face.

00:35 So, the parabola has a maximum point at the top.

00:39 And that's how we solve this problem!

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