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Formulas Equation of a line: When you have one point and slope 𝑦 − 𝑦! = 𝑚(𝑥 − 𝑥! ) where m = slope When you have two points 𝑦" − 𝑦! 𝑆𝑙𝑜𝑝𝑒 = 𝑚 =...

Formulas Equation of a line: When you have one point and slope 𝑦 − 𝑦! = 𝑚(𝑥 − 𝑥! ) where m = slope When you have two points 𝑦" − 𝑦! 𝑆𝑙𝑜𝑝𝑒 = 𝑚 = 𝑥" − 𝑥! 𝑦 − 𝑦! = 𝑚(𝑥 − 𝑥! ) where m = slope Exponents: 𝑋 #. 𝑋 $ = 𝑋 #%$ 𝑋# = 𝑋 #&$ 𝑋$ (𝑎. 𝑏)' = 𝑎'. 𝑏 ' 𝑎 ' 𝑎' 2 3 = ' 𝑏 𝑏 1 𝑋' = 𝑋 &' 1 𝑋 &' = 𝑋' ! ( √𝑋 ( = 𝑋 ' Solving Quadratic Equation (𝑎𝑥 " + 𝑏𝑥 + 𝑐 = 0) −𝑏 ± √𝑏 " − 4. 𝑎. 𝑐 𝑥= 2. 𝑎 3 Forms of Quadratic Expressions: 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐹𝑜𝑟𝑚: 𝑎𝑥 " + 𝑏𝑥 + 𝑐 where c = vertical intercept 𝐹𝑎𝑐𝑡𝑜𝑟𝑒𝑑 𝐹𝑜𝑟𝑚: 𝑎(𝑥 − 𝑟). (𝑥 − 𝑠) where, r and s are zeroes 𝑉𝑒𝑟𝑡𝑒𝑥 𝐹𝑜𝑟𝑚: 𝑎(𝑥 − ℎ)" + 𝑘 where, (h,k) = vertex 𝐼𝑓 𝑎 > 0 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑔𝑟𝑎𝑝ℎ(𝑝𝑎𝑟𝑎𝑏𝑜𝑙𝑎) 𝑜𝑝𝑒𝑛𝑠 𝑢𝑝. 𝐼𝑓 𝑎 < 0 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑔𝑟𝑎𝑝ℎ(𝑝𝑎𝑟𝑎𝑏𝑜𝑙𝑎) 𝑜𝑝𝑒𝑛𝑠 𝑑𝑜𝑤𝑛. Logarithms ln(𝑥) = log ) (𝑥) log(𝑎. 𝑏) = log(𝑎) + log(𝑏) 𝑎 log 2 3 = log(𝑎) − log(𝑏) 𝑏 log(𝑎* ) = 𝑡. log(𝑎) log $ (𝑏) = 1 𝐸𝑔. log(10) = 1 log(1) = 0 log(10+ ) = 𝑁 ln(𝑒 , ) = log ) (𝑒 , ) = 𝑥 log $ (𝑥) = 𝑦 𝑚𝑒𝑎𝑛𝑠 𝑥 = 𝑏- log(𝑥) log $ (𝑥) = log(𝑏) Exponential Functions: § If the question mentions continuous growth rate o 𝑄 = 𝑎. 𝑒.* where k = continuous growth rate o 𝑎 = 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 o 𝑄 = 𝑜𝑢𝑡𝑝𝑢𝑡 § If the question just mentions growth rate o 𝑄 = 𝑎𝑏 * o 𝑎 = 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 o 𝑏 = 𝑔𝑟𝑜𝑤𝑡ℎ 𝑓𝑎𝑐𝑡𝑜𝑟 = 𝑟 + 1 o 𝑟 = 𝑔𝑟𝑜𝑤𝑡ℎ 𝑟𝑎𝑡𝑒 = 𝑏 − 1 § If the question mentions decrease/decay o 𝑄 = 𝑎𝑏 * o 𝑎 = 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 o 𝑏 = 𝑟𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 (𝑜𝑟 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛) o 𝑏 = 𝑔𝑟𝑜𝑤𝑡ℎ 𝑓𝑎𝑐𝑡𝑜𝑟 = 𝑟 + 1 o 𝑟 = 𝑔𝑟𝑜𝑤𝑡ℎ 𝑟𝑎𝑡𝑒 = 𝑏 − 1