Yes but it is not a straight line because it looks like an umbrella and it is called a parabola
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It is the axis of symmetry.
No vertical line will intersect the graph in more than one point. The fundamental flaw is that no graph can show that it does not happen beyond the domain of the graph.
The parabola
The real solutions are the points at which the graph of the function crosses the x-axis. If the graph never crosses the x-axis, then the solutions are imaginary.
No. It can also be a circle, ellipse or hyperbola.