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There are two distinct real solutions.
Two distinct real solutions.
If the discriminant > 0 then 2 distinct real solutions.If the discriminant = 0 then 1 double real solution.If the discriminant < 0 then no real solutions (though there are two complex solutions).
The form is not specified in the question so it is hard to tell. But two parabolas with different vertices can certainly have the same axis of symmetry.
There are two ways of classifying parabolas: By the direction in which they are open: open at the top or at the bottom. By the number of real roots: 2 real, 1 real or no real roots.