Find the intervals where the function is increasing:
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Find the intervals where the function is increasing:
To solve this problem, we need to determine where the function is increasing.
Step 1: Notice that the given function is in the form , which indicates it is a quadratic function.
Step 2: The coefficient , 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 , where and . Thus, the vertex is at .
Step 4: For a downward-opening parabola, the function is increasing on the left side of the vertex. Hence, the function is increasing for .
Therefore, the intervals where the function is increasing is .
The correct answer is: .
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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