Find Increasing Intervals for y = -(x-14)^2 - 6: Vertex Form Quadratic

Find the intervals where the function is increasing:

y=(x14)26 y=-(x-14)^2-6

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1

Understand the problem

Find the intervals where the function is increasing:

y=(x14)26 y=-(x-14)^2-6

2

Step-by-step solution

To solve this problem, we need to determine where the function y=(x14)26 y = -(x-14)^2 - 6 is increasing.

Step 1: Notice that the given function is in the form y=a(xh)2+k y = a(x-h)^2 + k , which indicates it is a quadratic function.

Step 2: The coefficient a=1 a = -1 , so the parabola opens downwards. This implies the function decreases to the left of the vertex and increases to the right.

Step 3: Identify the vertex of the parabola. The vertex form is (h,k) (h, k) , where h=14 h = 14 and k=6 k = -6 . Thus, the vertex is at (14,6) (14, -6) .

Step 4: For a downward-opening parabola, the function is increasing on the left side of the vertex. Hence, the function is increasing for x<14 x < 14 .

Therefore, the intervals where the function is increasing is x<14 x < 14 .

The correct answer is: x < 14\textbf{x < 14}.

3

Final Answer

x<14 x<14

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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