These are all quadratic equations
[tex]y = ax^{2} + bx + c[/tex]
so you can use the formula
[tex] R = b^{2} - 4ac[/tex]
to determine the number of real answers.
If R < 0, there is 0 real solution.
If R = 0, there is 1 real solution.
If R > 0, there are 2 real solutions.
Let me do the first one :
[tex]y = -3x^{2} + x + 12[/tex]
You find
[tex]R = 1^{2} - 4 \times (-3) \times 12 > 0[/tex]
Thus this equation has two real solutions.
