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

Question

Find the descending area of the function

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

Video Solution

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 .

Answer

x < -2