Find the Area Under (x+2)²-1: Quadratic Function Analysis

Find the descending area of the function

y=(x+2)21 y=(x+2)^2-1

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Find the descending area of the function

y=(x+2)21 y=(x+2)^2-1

2

Step-by-step solution

To solve this problem, we'll determine where the function y=(x+2)21 y = (x+2)^2 - 1 is decreasing. This function is a parabola of the form y=(xh)2+k y = (x-h)^2 + k , with h=2 h = -2 and k=1 k = -1 .

The vertex of this parabola is at (2,1) (-2, -1) . Since the coefficient of the squared term (x+2)2(x+2)^2 is positive, the parabola opens upwards. This tells us that the function decreases to the left of the vertex and increases to the right.

Therefore, the function is decreasing for x<2 x < -2 .

In the context of this multiple-choice question, the decreasing interval corresponds to the choice: x<2 x < -2 .

Thus, the descending region for the function is x<2 x < -2 .

3

Final Answer

x<2 x < -2

Practice Quiz

Test your knowledge with interactive questions

Which equation represents the function:

\( y=x^2 \)

moved 2 spaces to the right

and 5 spaces upwards.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Parabola Families questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations