The point where a graph intercepts the x axis may have several names. It could be called an x-intercept, a root, or a solution.It is at: (x, 0).
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That could be the x-intercept of the graph, or
a root or solution of the equation graphed.
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Just one. It's at the origin. (0, 0)
Yes, the places where the graph of a polynomial intercepts the x-axis are zeros. The value of y at those places must be 0 for the polynomial to intersect the x axis.
The quadratic equation is used to find the intercepts of a function (F(x)=x^(2*n), n being an even number) along its primary axis (typically the x axis). Many equations follow this form. The information given by the quadratic equation depends on what your function is pertaining to. If say you have a velocity vs time graph, when the function crosses the xaxis your particle has changed from a positive velocity to a negative velocity. This information can be useful to determine the accompanying behavior of your position. The quadratic equation is simply a tool to find intercepts of a function.
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