Finding Decreasing Intervals: Parabola with Vertex at x = 4

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

Find the intervals where the function is decreasing

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1

Understand the problem

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

Find the intervals where the function is decreasing

2

Step-by-step solution

To solve this problem, we'll consider the following:

  • Understand that the vertex form of a parabola, located at point x=4 x = 4 , gives critical information about its symmetry line and vertex location.
  • The parabola can either open upwards or downwards, determined by the sign of a a in the quadratic equation y=ax2+bx+c y = ax^2 + bx + c .
  • If a>0 a > 0 , the parabola opens upwards, meaning it decreases for x<4 x < 4 and increases for x>4 x > 4 .
  • If a<0 a < 0 , the parabola opens downwards, meaning it increases for x<4 x < 4 and decreases for x>4 x > 4 .
  • Given only the vertex x=4 x = 4 , we lack the information about the parabola's opening without the value of a a .

Therefore, it cannot be determined whether the function is decreasing on any specific interval without knowing the sign of a a .

The correct choice is Cannot be determined.

3

Final Answer

Cannot be determined

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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