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The invariant points here are not the turning points as in the reciprocal of linear functions.
The invariant points are points that remain the same for both the quadratic function and its reciprocal function. They are not the turning points in this case, but must be points on the reciprocal functions.
Therefore, when asked to graph the reciprocal function of a quadratic function, you can first draw the quadratic function to locate the invariant points.
When sketch the graph, just follow the shape for reciprocal of a quadratic function with no zero, one zero or two zeros, and make sure the graph passes through the invariant points.
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