They open up and will be symmetrical across the y-axis.
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All quadratic functions with real coefficients can be graphed on a standard x-y graph. Not all quadratic functions have real roots, maybe that's what you were thinking of?
The graph (on Cartesian coordinates) of a quadratic equation is a parabola.
Equations are not linear when they are quadratic equations which are graphed in the form of a parabola
There are linear functions and there are quadratic functions but I am not aware of a linear quadratic function. It probably comes from the people who worked on the circular square.
There are different methods of using quadratic functions depending on the equation.