Finding Intervals of Increase for a Parabola with Vertex at x = 4

The vertex of the smiling parabola is located at the point x=4 x=4

Find the intervals of increase of the function

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1

Understand the problem

The vertex of the smiling parabola is located at the point x=4 x=4

Find the intervals of increase of the function

2

Step-by-step solution

To determine the intervals of increase for the given "smiling" parabola with a vertex at x=4 x = 4 , follow these steps:

  • Since the parabola is described as "smiling," it opens upwards, which means it has its minimum at the vertex.
  • The function decreases in the interval to the left of the vertex and increases to the right of it.
  • Thus, the parabola is increasing for x>4 x > 4 .

Therefore, the correct interval of increase for the function is x>4 x > 4 .

3

Final Answer

x>4 x>4

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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