Calculate Negative Area Under y=(x+2)²: Quadratic Function Analysis

Question

Find the negative area of the function

$y=(x+2)^2$

Video Solution

Solution Steps

00:00 Find the negative domain of the function

00:03 Use shortened multiplication formulas and open parentheses

00:08 Look at the coefficient of X squared, positive

00:12 When the coefficient is positive, the function smiles

00:15 Now we want to find the intersection points with the X-axis

00:20 At the intersection points with X-axis, Y=0, substitute and solve

00:24 Take out the root to get rid of the power

00:27 Isolate X

00:32 This is the X value at the intersection point with X-axis

00:37 Draw the function according to intersection points and function type

00:45 The function is positive while it's above the X-axis

00:51 And this is the solution to the question

Step-by-Step Solution

The function $y = (x+2)^2$ describes a parabola that opens upwards and has its vertex at $(-2, 0)$ . Since the equation involves a perfect square, it yields only non-negative values for all $x$ and always lies on or above the x-axis. Therefore, there is no part of this parabola that crosses below the x-axis, resulting in no "negative area" above or below the x-axis.

In conclusion, the correct answer among the choices is: There is no negative area.

Answer

There is no

Related Subjects

Family of Parabolas y=(x-p)² Families of Parabolas

Question Types

Parabola of the Form y=(x-p)²: Identify the positive and negative domain