To determine which point is a turning point of the graph of the function \( y = x(x + 1)(x - 1)(x - 3) \), we can use the information about local extrema from the graph you described.
Turning points occur where the graph changes direction, which typically happens at local maxima or minima.
Given that the graph has two minimum values and one maximum value, we can analyze the points:
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Point A (−1, 0): This point is on the x-axis but is not a turning point (it does not indicate a change in direction).
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Point B (0.5, 1): This point lies above the x-axis and could potentially be a local maximum, but without further information about the graph's behavior before and after this point, we can't confirm if it's a turning point.
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Point C (1.5, −3): This point is a local minimum as indicated in the description of the graph, which means it is a turning point.
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Point D (3, 0): This point is also on the x-axis but is not specifically indicated as a turning point in the problem.
Based on the information provided, Point C (1.5, -3) is confirmed to be a turning point because it corresponds with one of the local minima noted in the graph you described.
So the answer is C.
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