A quadratic equation is written as a system of a quadratic function and a linear function. Select the number of possible ways the graphs can intersect.

The intersections occur where the quadratic and linear functions have the same output. Setting them equal gives a quadratic equation, which can have zero, one, or two real solutions. Therefore, the graphs can intersect in 0, 1, or 2 points; they cannot intersect infinitely many times because a line and a quadratic are distinct functions.

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