For sake of saving time, <= means less than or equal to, >= means greater
than or equal to.
inf. will often be used to indicate infinity.
Interval notation
[a,b] means a <= x <= b.
(a,b) means a < x < b.
[a,b) means a <= x < b.
Line equations
When given two coordinates on a line, (x_1,y_1) (x_2,y_2)v, m, the slope of a line, can be found by the change in y over the change in x. | |
This equation is referred to as the point-slope form of a line. Notice there is only one coordinate used, (x_1,y_1). | |
This is referred to as the slope-intercept form, or y-intercept form. b is the y-intercept. | |
The distance, D, between two points, (x_1,y_1) and (x_2,y_2) can be found by this equation. | |
This is the standard form for the equation of a circle with center at (h,k). r denotes the radius. | |
This is the quadratic formula, used to solve for the roots of a function such that f(x) = ax^2+bx+c |
Lines are parallel when their slope are the same but have different intercepts.
Lines are perpindicular when their slopes are such that m_1*m_2 = -1.
Completing the square of an equation x^2+bx = 0 is easy. Take half
the linear coefficient, bx, and square it, adding that to both sides. The left
side factors to (x+b/2)^2 = b^2/4
Functions
Functions produce a unique output f(x) from an input x. This means that the
graph of a function must have the property that any vertical line can intersect
the graph of the function at most once.