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What is the relationship between the roots of a quadratic, and the x-intercepts of the quadratic?

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The roots of a quadratic are the x-intercepts of its graph.  If there is only one (double root), then the x-intercept is the vertex of the parabola.  If there is no real root (two imaginary roots), then the parabola does not cross the x axis (there are no x-intercepts).