Find Decreasing Intervals: Analyzing y = (x+8)² - 1

Find the intervals where the function is decreasing:

y=(x+8)21 y=(x+8)^2-1

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1

Understand the problem

Find the intervals where the function is decreasing:

y=(x+8)21 y=(x+8)^2-1

2

Step-by-step solution

The function given is y=(x+8)21 y = (x+8)^2 - 1 , which is in vertex form. The vertex of this parabola is at (8,1) (-8, -1) .

Since the coefficient of (x+8)2(x+8)^2 is positive (+1+1), the parabola opens upwards. This means that the function is decreasing to the left of the vertex.

In mathematical terms, the function is decreasing when x x is less than the vertex x x -coordinate, x=8 x = -8 .

Therefore, the function is decreasing for the interval x<8 x < -8 .

3

Final Answer

x<8 x<-8

Practice Quiz

Test your knowledge with interactive questions

Note that the graph of the function shown below does not intersect the x-axis

The parabola's vertex is A

Identify the interval where the function is decreasing:

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