Parallel/Perpendicular lines
If you have a line y = 2x + 1
A Parallel line is: y = 2x + anything
A Perpendicular line is: y = -1/2x + anything (use the negative reciprocal of the slope)
Parabolas
Two primary notations:
Standard form: y = ax^2 + bx + c axis of symmetry is -b/2a
Vertex form: y = a(x-h)^2 + k vertex is located at (h,k)
To convert standard to vertex, complete the square. To convert vertex to standard, expand the square.
Circles
Standard form: (x - h)^2 + (y - k)^2 = r^2
The center is located at (h, k)
The radius is r
Sometimes, to get an equation of a cirlce to standard form, you will need to complete the square for both x and y.
Comparing two points
You can find the distance between two points by drawing a right triangle and using (x1 - x2)^2 - (y1 - y2)^2 = c^2
You can find the midpoint between two points with m = ((x1 + x2)/2, (y1+y2)/2)