here. You'll also need to know how to solve quadatic equations; the Quadratic Formula may prove helpful.
To learn how to find domains and ranges, try here. The domain is pretty obvious, since the function is a polynomial. To find the specific range here, you'll need to complete the square to convert the quadratic to "vertex" form. Then copy down the vertex. Use the fact that this quadratic is negative to determine whether the vertex gives the maximal value (and thus the upper limit of the range) or the minimal value (and thus the lower limit of the range).
The axis of symmetry is the vertical line through the vertex.
If you get stuck, please reply showing what you have tried so far. Thank you!