What is each formula used for? Just need brief explanations.

If P

_{1}has coordinates (x_{1}, y_{1}) and P_{2}has coordinates (x_{2}, y_{2}), then the distance between the two points isgiven by [(x

_{1}- x_{2})^{2}+ (y_{1}- y_{2})^{2}]^{½}or [(x_{2}- x_{1})^{2}+ (y_{2}- y_{1})^{2}]^{½}Using the same two points as above, the midpoint formula is

M = [(x

_{1}+ x_{2})/2], [(y_{1}+ y_{2})/2]If we wanted to find the slope of the line on which the two points lie, it would be given by:

m = (y

_{1}- y_{2})/(x_{1}- x_{2}) or (y_{2}- y_{1})/(x_{2}- x_{1})Some quadratic equations can be easily factored, some cannot. For those cases we use the Quadratic Formula:

If ax

^{2}+ bx + c = 0then x = [-b ± (b

^{2}- 4ac)^{½}]/2aNotice that the Distance, Midpoint and Slope Formulas all refer to linear equations. The quadratic formula, as the name implies, is used to find roots of an equation in which the variable x is squared.