[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522673-105":59,"doc-detail-522673-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","graphing-polynomial-functions-basic-shape-algebra-2-worksheet","Graphing Polynomial Functions: Basic Shape - Algebra 2 Worksheet","","Algebra 2 worksheet focused on graphing polynomial functions by analyzing end behavior and sketching the general graph shape. Problems include polynomials with various degrees and signs, asking for the direction of both ends and the maximum number of turns the graph can make. Students also sketch the overall shape for multiple functions, distinguishing behaviors such as rising or falling ends and using degree-based turning rules to predict graph complexity.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/graphing-polynomial-functions-basic-shape-algebra-2-worksheet/522673/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/graphing-polynomial-functions-basic-shape-algebra-2-worksheet/522673.png","ImageObject",300,407,{"name":92,"@type":93},"Mia  ","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you determine the end behavior of a polynomial function on this worksheet?","Question",{"text":112,"@type":113},"Use the leading term and its degree to decide whether f(x) approaches +∞ or −∞ as x goes to +∞ and −∞ for each function.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is the “maximum number of turns” the graph of a polynomial could make?",{"text":117,"@type":113},"For a polynomial, the maximum number of turning points is based on its degree; the worksheet uses this to predict how many direction changes the graph can have.",{"name":119,"@type":110,"acceptedAnswer":120},"What does “sketch the general shape” require for these polynomial functions?",{"text":121,"@type":113},"Sketch the overall graph form using the end behavior and the turning-point limit, matching the polynomial’s degree and leading-term behavior.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},522673,1791732423,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":52,"preview_page_count":4},687207024478,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Kuta Software-Infinite Algebra 2 Name___________________________________  \nGraphing Polynomial Functions: Basic Shape Date________________ Period____  \nDescribe the end behavior of each function.  \n1) f (x) = x 3 − 4x2 + 7 2) f (x) = x 3 − 4x2 + 4  \n3) f (x) = x 3 − 9x2 + 24x − 15 4) f (x) = x 2 − 6x + 11  \n5) f (x) = x 5 − 4x3 + 5x + 2 6) f (x) = −x2 + 4x  \n7) f (x) = 2x2 + 12x + 12 8) f (x) = x 2 − 8x + 18  \nState the maximum number of turns the graph of each function could make.  \n9) f (x) = x 5 − 4x3 + 5x + 1 10) f (x) = −x2 − 1  \nSketch the general shape of each function.  \n11) f (x) = −x2 − 6x − 7 12) f (x) = x 3 − 2x2 + 1  \n13) f (x) = x 2 + 2 14) f (x) = −x4 + 3x3 − 2 − 5x  \n15) f (x) = −x5 + 4x3 − x + 1 16) f (x) = x 3 − 2x2 − 3  \n17) f (x) = −x5 + 3x3 + 2 18) f (x) = −x3 + 10x2 − 33x + 32  \nKuta Software-Infinite Algebra 2 Name___________________________________  \nGraphing Polynomial Functions: Basic Shape Date________________ Period____  \nDescribe the end behavior of each function.  \n1) f (x) = x 3 − 4x2 + 7 2) f (x) = x 3 − 4x2 + 4  \nf (x) → −∞ as x → −∞ f (x) → −∞ as x → −∞  \nf (x) → +∞ as x → +∞ f (x) → +∞ as x → +∞  \n3) f (x) = x 3 − 9x2 + 24x − 15 4) f (x) = x 2 − 6x + 11  \nf (x) → −∞ as x → −∞ f (x) → +∞ as x → −∞  \nf (x) → +∞ as x → +∞ f (x) → +∞ as x → +∞  \n5) f (x) = x 5 − 4x3 + 5x + 2 6) f (x) = −x2 + 4x  \nf (x) → −∞ as x → −∞ f (x) → −∞ as x → −∞  \nf (x) → +∞ as x → +∞ f (x) → −∞ as x → +∞  \n7) f (x) = 2x2 + 12x + 12 8) f (x) = x 2 − 8x + 18  \nf (x) → +∞ as x → −∞ f (x) → +∞ as x → −∞  \nf (x) → +∞ as x → +∞ f (x) → +∞ as x → +∞  \nState the maximum number of turns the graph of each function could make.  \n9) f (x) = x 5 − 4x3 + 5x + 1 10) f (x) = −x2 − 1  \nMax \\# Turns: 4 Max \\# Turns: 1  \nSketch the general shape of each function.  \n11) f (x) = −x2 − 6x − 7 12) f (x) = x 3 − 2x2 + 1  \n13) f (x) = x 2 + 2 14) f (x) = −x4 + 3x3 − 2 − 5x  \n15) f (x) = −x5 + 4x3 − x + 1 16) f (x) = x 3 − 2x2 − 3  \n17) f (x) = −x5 + 3x3 + 2  \n18) f (x) = −x3 + 10x2 − 33x + 32  \nCreate your own worksheets like this one with Infinite Algebra 2. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCairckFHkiE3yA","https://ap.wps.com/l/cbCairckFHkiE3yA","pdf",37622,"English","# Describe end behavior of each function\n## Max number of turns\n# Sketch the general shape of each function","[{\"question\":\"How do you determine the end behavior of a polynomial function on this worksheet?\",\"answer\":\"Use the leading term and its degree to decide whether f(x) approaches +∞ or −∞ as x goes to +∞ and −∞ for each function.\"},{\"question\":\"What is the “maximum number of turns” the graph of a polynomial could make?\",\"answer\":\"For a polynomial, the maximum number of turning points is based on its degree; the worksheet uses this to predict how many direction changes the graph can have.\"},{\"question\":\"What does “sketch the general shape” require for these polynomial functions?\",\"answer\":\"Sketch the overall graph form using the end behavior and the turning-point limit, matching the polynomial’s degree and leading-term behavior.\"}]","Graphing Polynomial Functions: Basic Shape - Algebra 2 Worksheet | PDF",1791426046]