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

Find the negative area of the function

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
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 written solution

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1

Understand the problem

Find the negative area of the function

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

2

Step-by-step solution

The function y=(x+2)2 y = (x+2)^2 describes a parabola that opens upwards and has its vertex at (−2,0) (-2, 0) . Since the equation involves a perfect square, it yields only non-negative values for all x 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.

3

Final Answer

There is no

Practice Quiz

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Find the intersection of the function

\( y=(x+4)^2 \)

With the Y

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