College Algebra Formulas and Rules

Standard Form (Linear)
General Form (Quadratic)
Difference of Squares
𝑨𝒙 + π‘©π’š = π‘ͺ
π’‚π’™πŸ + 𝒃𝒙 + 𝒄 = π’š 𝒐𝒓
𝒇(𝒙) = π’‚π’™πŸ + 𝒃𝒙 + 𝒄; 𝒇(𝒙) ≑ π’š
(π’™πŸ βˆ’ π’šπŸ ) = (𝒙 βˆ’ π’š)(𝒙 + π’š)
Standard (Vertex) Form
π’š βˆ’ π’šπŸ = π’Ž(𝒙 βˆ’ π’™πŸ )
𝒇(𝒙) = 𝒂(𝒙 βˆ’ 𝒉)𝟐 + π’Œ
Slope-Intercept Form
π’Ž=
π’šπŸ βˆ’ π’šπŸ
π’™πŸ βˆ’ π’™πŸ
(𝒉, π’Œ) = οΏ½
𝒅 = οΏ½(π’™πŸ βˆ’ π’™πŸ )𝟐 + (π’šπŸ βˆ’ π’šπŸ )𝟐
π’“πŸ = (𝒙 βˆ’ 𝒉)𝟐 + (π’š βˆ’ π’Œ)𝟐
𝒙 𝟏 + 𝒙 𝟐 π’šπŸ + π’šπŸ
οΏ½
,
οΏ½
𝟐
𝟐
𝒓 = οΏ½(𝒙 βˆ’ 𝒉)𝟐 + (π’š βˆ’ π’Œ)𝟐
r = radius, (h, k) = center of circle
𝒙𝒛 𝒏
𝒙𝒛𝒏
οΏ½ 𝒛 οΏ½ = 𝒛𝒏
𝟎
π’š
π’š
𝟎 = 𝒖𝒏𝒅𝒆𝒇.
π’šβ‰ πŸŽ
𝟏
βˆ’π’
𝒙 = 𝒏
(𝒙𝒛 )𝒏 = 𝒙𝒛𝒏
𝒙
π’™β‰ πŸŽ
(π’™π’š)𝒛 = 𝒙𝒛 π’šπ’›
π’™πŸŽ = 𝟏
𝒏
βˆšπ’™ = π’™πŸ/𝒏 ; n β‰  𝟎
𝒛
𝒏
𝒏
οΏ½ βˆšπ’™οΏ½ = βˆšπ’™π’› = 𝒙𝒛/𝒏
π’š = log 𝒃 𝒙 ⟺ π’ƒπ’š = 𝒙
π₯𝐨𝐠 𝒂 𝒃
LSC-O Learning Center
βˆ’π’ƒ
βˆ’π’ƒ
βˆ’π’ƒ
π’ƒπŸ
, 𝒇 οΏ½ οΏ½οΏ½ 𝒐𝒓 οΏ½
,𝒄 βˆ’ οΏ½
πŸπ’‚
πŸ’π’‚
πŸπ’‚
πŸπ’‚
Equation of a Circle
Midpoint Formula
π₯𝐨𝐠 𝒃 π’š =
Difference of Cubes
Vertex of a Parabola
Distance Formula
π₯𝐨𝐠 𝒂 π’š
π’™πŸ + πŸπ’™π’š + π’šπŸ = (𝒙 + π’š)𝟐
π’™πŸ βˆ’ πŸπ’™π’š + π’šπŸ = (𝒙 βˆ’ π’š)𝟐
βˆ’π’ƒ ± βˆšπ’ƒπŸ βˆ’ πŸ’π’‚π’„
𝒙=
πŸπ’‚
Slope Formula
π’™πŸ + π’šπŸ ; π’‘π’“π’Šπ’Žπ’†
Perfect Square Trinomial
Quadratic Formula
π’š = π’Žπ’™ + 𝒃
Sum of Squares
π’™πŸ‘ βˆ’ π’šπŸ‘ = (𝒙 βˆ’ π’š)οΏ½π’™πŸ + π’™π’š + π’šπŸ οΏ½
Sum of Cubes
π’™πŸ‘ + π’šπŸ‘ = (𝒙 + π’š)οΏ½π’™πŸ βˆ’ π’™π’š + π’šπŸ οΏ½
β–² Tip: Use S.O.A.P. to remember
the signs in the Diff. and Sum of
Cubes formulasβ€”Same, Opposite,
Always Positive.
π‘₯𝑛
π‘›βˆ’π‘§
=
π‘₯
π‘₯𝑧
π‘₯β‰ 0
Find this and other math
resources on the LSC-O
Learning Center Math
Tutorials page.
𝒙𝒛 𝒙𝒏 = 𝒙𝒛+𝒏
http://www.lsco.edu/learningcenter/math.asp
𝒙𝒏 + 𝒙𝒏 = πŸπ’™π’
οΏ½
πŸπ’™π’ βˆ’ 𝒙𝒏 = 𝒙𝒏
π₯𝐨𝐠 𝒃 𝟏 = 𝟎; π₯𝐨𝐠 𝟎 = 𝒖𝒏𝒅𝒆𝒇.
𝒃
π₯𝐨𝐠 𝒃 𝒃𝒙 = 𝒙
β—„Tip: Use the change of base formula to
convert to base 10 (log) or base e (ln).
Some calculators handle only these
bases.
(409) 882-3373
𝒙
βˆšπ’™
=
; π’š β‰ πŸŽ
π’š
π’š
οΏ½
π₯𝐨𝐠 𝒃 𝒃 = 𝟏
𝒃log𝒃 𝒙 = 𝒙
π₯𝐨𝐠 𝒃 𝑴𝒑 = 𝑷 π₯𝐨𝐠 𝒃 𝑴
π₯𝐨𝐠 𝒃 𝒙 = π₯𝐨𝐠 𝒃 π’š β†’ 𝒙 = π’š
π₯𝐨𝐠 𝒃 𝑴𝑡 = π₯𝐨𝐠 𝒃 𝑴 + π₯𝐨𝐠 𝒃 𝑡
𝑴
π₯𝐨𝐠 𝒃 = π₯𝐨𝐠 𝒃 𝑴 βˆ’ π₯𝐨𝐠 𝒃 𝑡
𝑡
Ron E. Lewis Library building, rm. 113
EP, 7/2013
Point-Slope Formula