Algebra
How can you tell an equation's real or imaginary roots just from its graph, without knowing the equation? I have to look ath the graph of a parabola, absolute value, and a negative third degree equation and do so? Are there any links that could explain this as I can't scan in the problems to show you? Or could you just make a generalization?
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Answers
Generally speaking, the graph of a function with real roots will have an x-intercept (where the graph intersects the x-axis), while a graph of a function with imaginary roots will not have an x-intercept. For a parabola, if the graph is "opening up" then it will have a single real root, and if it is "opening down" then it will not have any real roots. For an absolute value graph, if the graph is "opening up" then it will have two real roots, and if it is "opening down" then it will not have any real roots. For a negative third degree equation, if the graph is "opening up" then it will have three real roots, and if it is "opening down" then it will not have any real roots.
