A quadratic equation is written as a system of two quadratic functions. Select the number of possible ways the graphs can intersect.

Intersections occur where the two functions have the same y-value. Setting their quadratic expressions equal gives an equation of degree at most 2, so there can be 0, 1, or 2 intersection points. If the two functions are identical, their graphs overlap completely and have infinitely many intersection points. Thus all four choices are possible.

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