[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-571855-105":53,"doc-detail-571855-en":126},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":119,"head_meta":121,"extra_data":123,"updated_unix":125},105,"en","algebra-cheat-sheet-basic-properties-facts-functions-and-graphs","Algebra Cheat Sheet - Basic Properties & Facts - Functions and Graphs","","Algebra Cheat Sheet compiles core algebra reference rules for quick review and problem solving. It summarizes arithmetic operations, exponent properties, radicals, inequalities, absolute value, and key complex number relationships. The sheet also covers logarithm definitions and log properties, factoring and solving formulas including quadratic and square root methods, completing the square, and common errors. It further provides function forms and graph characteristics for lines and conics, plus distance and geometry-related formulas.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":46,"@type":70,"position":76},"https://docshare.wps.com/template/paper-templates/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/algebra-cheat-sheet-basic-properties-facts-functions-and-graphs/571855/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/algebra-cheat-sheet-basic-properties-facts-functions-and-graphs/571855.png","ImageObject",442,249,{"name":88,"@type":89},"Oliver","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-15","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":9},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What are the main sections covered in the Algebra Cheat Sheet?","Question",{"text":108,"@type":109},"It covers basic properties and facts, complex numbers, logarithms and log properties, factoring and solving, functions and graphs, and a list of common algebraic errors.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"How are complex numbers handled in the cheat sheet?",{"text":113,"@type":109},"It defines i via i = -1 and provides operations for sums, differences, products, plus relationships for the complex conjugate and modulus.",{"name":115,"@type":106,"acceptedAnswer":116},"What solving tools are included for quadratic and related equations?",{"text":117,"@type":109},"It includes the quadratic formula, square root property usage, and a completing-the-square procedure illustrated with steps for transforming the equation.","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},571855,1792053967,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":45,"category_name":46,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":9,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":135,"language":136,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":61,"update_tm":140,"read_time":141},8796095461610,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Algebra Cheat Sheet  \nBasic Properties & Facts  \nArithmetic Operations ab + ac = a (b + c )  \na  \n~~ ~~bc~~ ~~ = abc  \nab + ~~ ~~cd = ~~ ~~adbbc acbd = ~~ ~~bd~~ ~~ac  \nab + ac  \n= b + c, a ≠ 0 a  \nExponent Properties anam = an +m  \n((anab))mn  aannmbna −n = ~~ ~~a1n~~ ~~  \n− na  \nb  \nb n bn  \n= a~~ ~~ =  an  \na b  =  abc c  \n~~ ~~ab~~ ~~ = ~~ ~~acb  \ncab − ~~ ~~cd = ~~ ~~adbbc  \na + b a b ~~ ~~ =  +~~  ~~c c c  \na  \n~~ ~~bc~~ ~~ = ~~ ~~abdcd  \naanm~~ ~~ = an −m = ~~ ~~a~~ ~~~~−~~n~~ ~~  \na 0 = 1 , a ≠ 0 n n  \nab~~ ~~ = ~~ ~~abn~~ ~~an~~ ~~ = an  \na nm = (a 1m ) = (an)  \nn  1  \n  m  \nProperties of Radicals  \n= a, if n is odd  \n  = a  , if n is even  \nProperties of Inequalities  \nIf a \u003C b then a + c \u003C b + c and a − c \u003C b − c If a \u003C b and c > 0 then ac \u003C bc and a \u003C b  \nc c  \nIf a \u003C b and c \u003C 0 then ac > bc and a > b  \nc c  \nProperties of Absolute Value  \nif a ≥ 0  \nif a \u003C 0  \na + b  ≤ a  + b  Triangle Inequality  \nDistance Formula  \nIf P1 = (x1 , y1 ) and P2 = (x2 , y2 ) are two points the distance between them is  \nd (P1 , P2 ) =  \n (x2 − x1 )2 + (y2 − y1 )2  \nComplex Numbers  \ni = − 1 i 2 = − 1 −a = i, a ≥ 0 (a + bi ) + (c + di ) = a + c + (b + d )i  \n(a + bi ) − (c + di ) = a − c + (b − d )i (a + bi )(c + di ) = ac − bd + (ad + bc)i (a + bi )(a − bi ) = a2 + b2  \na + bi = + b2  Complex Modulus (a + bi ) = a − bi Complex Conjugate (a + bi )(a + bi ) = a + bi 2  \nFor a complete set of online Algebra notes visit [http://tutorial.math.lamar.edu](http://tutorial.math.lamar.edu). © 2005 Paul Dawkins  \nLogarithms and Log Properties Definition  \ny = logb x is equivalent to x = by  \nExample  \nlog5 125 = 3 because 53 = 125  \nSpecial Logarithms  \nln x = log e x natural log log x = log10 x common log where e = 2.718281828K  \nLogarithm Properties logb b = 1 logb 1 = 0 logb bx = x blogb x = x logb (xr)= r logb x  \nlogb (xy ) = logb x + logb y  \nlogb  \nxy~~ ~~ = logb x − logb y  \nThe domain of logb x is x > 0  \nFactoring and Solving  \nFactoring Formulas x2 − a2 = (x + a )(x − a ) x2 + 2ax + a2 = (x + a )2  \nx2 − 2ax + a 2 = (x − a )2  \nx2 + (a + b )x + ab = (x + a )(x + b ) x3 + 3ax2 + 3a2x + a 3 = (x + a )3  \nx3 − 3ax2 + 3a2 x − a 3 = (x − a )3  \nx3  \n3  \nx  \n+ a3 = (x + a )(x2 − ax +  \n− a 3 = (x − a )(x2 + ax +  \na2 )  \na2 )  \nx2n − a2n = (xn − an)(xn + an) If n is odd then,  \nxn − an = (x − a )(xn −1 + axn −2 + L + an −1 ) xn + an  \n= (x + a )(xn −1 − axn −2 + a 2xn −3 − L + an −1 )  \nQuadratic Formula  \nSolve ax2 + bx + c = 0 , a ≠ 0 x =  −b ± − 4ac  \n2a  \nIf b2 − 4ac > 0 -Two real unequal solns. If b2 − 4ac = 0 -Repeated real solution. If b2 − 4ac \u003C 0 -Two complex solutions.  \nSquare Root Property If x2 = p then x = ±  \nAbsolute Value Equations/Inequalities Ifb is a positive number  \nCompleting the Square  \nSolve 2x2 − 6x − 10 = 0  \n( 1) Divide by the coefficient ofthe x2 x2 − 3x − 5 = 0  \n(2) Move the constant to the other side. x2 − 3x = 5  \n(3) Take half the coefficient ofx, square it and add it to both sides  \n2 2  \nx2 − 3x + −  3  = 5 + −  3  = 5 +  9 =  29 2 2 4 4  \n(4) Factor the left side 2  \nx − ~~ ~~32~~ ~~ = ~~ ~~294  \n(5) Use Square Root Property x −  3 = ± = ±  29  \n2  4 2  \n(6) Solve for x  \nx =  3 ±  29  \n2 2  \nFor a complete set of online Algebra notes visit [http://tutorial.math.lamar.edu](http://tutorial.math.lamar.edu). © 2005 Paul Dawkins  \nFunctions and Graphs  \nConstant Function y = a or f (x ) = a  \nGraph is a horizontal line passing through the point (0, a ).  \nLine/Linear Function  \ny = mx + b or f (x ) = mx + b Graph is a line with point (0, b) and slope m.  \nSlope  \nSlope of the line containing the two points (x1 , y1 ) and (x2 , y2 ) is  \nm = ~~ ~~yx22~~ ~~~~ ~~yx11 = rren Slope – intercept form The equation of the line with slope mandy-intercept (0, b ) is  \ny = mx + b  \nPoint – Slope form  \nThe equation of the line with slope m  \nand passing through the point (x1 , y1 ) is y = y1 + m (x − x1 )  \nParabola/Quadratic Function  \ny = a (x − h )2 + k f (x ) = a (x − h )2 + k  \nThe graph is a parabola that opens","cbCaifml4CCxhQvh","https://ap.wps.com/l/cbCaifml4CCxhQvh","pdf",610249,25,"English","# Basic Properties & Facts\n## Arithmetic Operations\n## Exponent Properties\n## Properties of Radicals\n## Properties of Inequalities\n## Properties of Absolute Value\n# Complex Numbers\n## Complex Conjugate and Modulus\n# Logarithms and Log Properties\n# Factoring and Solving\n## Quadratic Formula\n## Completing the Square\n# Functions and Graphs\n## Slope Forms\n## Parabola/Quadratic Functions\n## Circle and Ellipse\n## Hyperbola\n# Common Algebraic Errors","[{\"question\":\"What are the main sections covered in the Algebra Cheat Sheet?\",\"answer\":\"It covers basic properties and facts, complex numbers, logarithms and log properties, factoring and solving, functions and graphs, and a list of common algebraic errors.\"},{\"question\":\"How are complex numbers handled in the cheat sheet?\",\"answer\":\"It defines i via i = -1 and provides operations for sums, differences, products, plus relationships for the complex conjugate and modulus.\"},{\"question\":\"What solving tools are included for quadratic and related equations?\",\"answer\":\"It includes the quadratic formula, square root property usage, and a completing-the-square procedure illustrated with steps for transforming the equation.\"}]","Algebra Cheat Sheet - Basic Properties & Facts - Functions and Graphs | PDF",1791924091,9]