There is one other important part of the parabola and it is called the latus rectum ...
It is the line the passes the the focus and ends at two points on the parabola. It lets you know how wide the parabola is supposed to be
Once you have drawn the Vertex and Latuc Rectum, you can...

Absolutely!
The simplest method is using the Quadratic Formula! Or at least that is my favorite!
x = [-b ± √(b2 - 4ac)]÷[2a]
Example 1: Let the equation be 3x2 + 11x - 4
Then ... a = 3, b = 11, c = -4
x = [-11 ± √(112 - (4)(3)(-4))]÷[(2)(3)]
x = [-11 ± √(121...

Multiply -1 to each term inside of the parentheses ...
= (-2)*(-1) - (c)*(-1)
= (2) - (-c)
= 2 + c

Combine the like terms ...
= 9x + 2 - 5x - 3
= 9x - 5x + 2 - 3
= 4x - 1