[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-522813-105":3,"doc-detail-522813-en":81,"detail-sidebar-cat-0-en-105":97},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","average-rates-of-change-worksheet","Average Rates of Change - Worksheet","","Practice worksheet for finding average rates of change of given quadratic functions over specified intervals and determining the equations of secant lines through pairs of points on each function. Includes multiple problems covering interval-based rate computation and secant-line intersection, plus a critical-thinking speed-limit scenario using two timestamps and highway distances to assess whether the evidence proves a violation. Designed for calculus skill reinforcement in Infinite Calculus context.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/average-rates-of-change-worksheet/522813/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/average-rates-of-change-worksheet/522813.png","ImageObject",300,407,{"name":42,"@type":43},"Alex Sinclair","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-11","2026-10-08",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",12,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How do you find the average rate of change over a given interval?","Question",{"text":63,"@type":64},"Compute the change in the function output over the interval and divide by the corresponding change in the input values.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What is a secant line in these problems?",{"text":68,"@type":64},"The secant line is the straight line that intersects the function at two given points, and its equation is determined from those points.",{"name":70,"@type":61,"acceptedAnswer":71},"Does the critical-thinking speed-limit question conclude the driver broke the limit?",{"text":72,"@type":64},"Yes. The provided reasoning states the average rate of change is 62 mph, implying the driver was breaking the speed limit some of the time.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},522813,1791497665,{"code":4,"msg":82,"data":83},"success",{"doc_id":79,"user_id":84,"nickname":42,"user_avatar":85,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":86,"file_id":87,"file_url":88,"file_type":89,"file_size":90,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":33,"language":91,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":92,"faqs":93,"seo_title":94,"seo_description":12,"update_tm":95,"read_time":96,"preview_page_count":4},1099523882182,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Kuta Software-Infinite Calculus Name   \nAverage Rates of Change Date  Period   \nFor each problem, find the average rate of change of the function over the given interval.  \n1) y = x 2 − x + 1; [0, 3]  \n2) y = − ~~ ~~x~~ ~~~~ ~~2~~ ~~ ; [−3, −2]  \nFor each problem, find the equation of the secant line that intersects the given points on the function.  \n3) y = − x 2 + x + 2; (−2, −4), ( 1, 2)  \n4) y = − ~~ ~~1x~~ ~~ ; ( 1, −1),(3, − ~~ ~~13)  \nFor each problem, find the average rate of change of the function over the given interval.  \n5) y = x 2 + 2; [−2, − ~~ ~~32] 6) y = 2x 2 − 2x + 1; [−1, − ~~ ~~12]  \n7) y = − ~~ ~~x~~ ~~~~ ~~2~~ ~~ ; [−1, − ~~ ~~12] 8) y = 2x 2 + x + 2; [0, ~~ ~~12]  \nFor each problem, find the equation of the secant line that intersects the given points on the function.  \n9) y = −x 2 − 2; ( 1, −3),(~~ ~~32~~ ~~ , − ~~ ~~174) 10) y = x~~ ~~~~ ~~3~~ ~~ ; (−1, ~~ ~~12),( − ~~ ~~12~~ ~~ , ~~ ~~25)  \n11) y = x~~ ~~~~ ~~1~~ ~~ ; (−2, − ~~ ~~13),(− ~~ ~~32~~ ~~ , − ~~ ~~25) 12) y = − ~~ ~~1x~~ ~~ ; ( 1, −1),(~~ ~~32~~ ~~ , − ~~ ~~23)  \nCritical thinking question:  \n13) The police have accused a driver of breaking the speed limit of 60 miles per hour. As proof, they provide two photographs. One photo shows the driver's car passing a toll booth at exactly 6 PM. The second photo shows the driver's car passing another toll both 31 miles down the highway at exactly 6:30 PM. Does the photo evidence prove that the driver broke the speed limit during this time?  \nKuta Software-Infinite Calculus Name   \nAverage Rates of Change Date  Period   \nFor each problem, find the average rate of change of the function over the given interval.  \n1) y = x 2 − x + 1; [0, 3]  \n2  \n2) y = − ~~ ~~x~~ ~~~~ ~~2~~ ~~ ; [−3, −2]  \n1  \n20  \nFor each problem, find the equation of the secant line that intersects the given points on the function.  \n3) y = − x 2 + x + 2; (−2, −4), ( 1, 2)  \ny = 2x  \n4) y = − ~~ ~~1x~~ ~~ ; ( 1, −1),(3, − ~~ ~~13)  \ny = ~~ ~~13x − 43  \nFor each problem, find the average rate of change of the function over the given interval.  \n5) y = x 2 + 2; [−2, − ~~ ~~32]  \n7  \n−  \n2  \n7) y = − ~~ ~~x~~ ~~~~ ~~2~~ ~~ ; [−1, − ~~ ~~12] 2  \n3  \n6) y = 2x 2 − 2x + 1; [−1, − ~~ ~~12]  \n−5  \n8) y = 2x 2 + x + 2; [0, ~~ ~~12] 2  \nFor each problem, find the equation of the secant line that intersects the given points on the function.  \n9) y = −x 2 − 2; ( 1, −3),(~~ ~~32~~ ~~ , − ~~ ~~174) 10) y = x~~ ~~~~ ~~3~~ ~~ ; (−1, ~~ ~~12),( − ~~ ~~12~~ ~~ , ~~ ~~25)  \ny = − ~~ ~~52x − 12~~ ~~ y = − ~~ ~~15x + ~~ ~~310  \n11) y = x~~ ~~~~ ~~1~~ ~~ ; (−2, − ~~ ~~13),(− ~~ ~~32~~ ~~ , − ~~ ~~25) 12) y = − ~~ ~~1x~~ ~~ ; ( 1, −1),(~~ ~~32~~ ~~ , − ~~ ~~23)  \ny = − ~~ ~~215x − ~~ ~~35~~ ~~ y = ~~ ~~23x − ~~ ~~53  \nCritical thinking question:  \n13) The police have accused a driver of breaking the speed limit of 60 miles per hour. As proof, they provide two photographs. One photo shows the driver's car passing a toll booth at exactly 6 PM. The second photo shows the driver's car passing another toll both 31 miles down the highway at exactly 6:30 PM. Does the photo evidence prove that the driver broke the speed limit during this time?  \nYes. The average rate of change is 62 mph, so the driver must have been breaking the speed  \nlimit some of the time.  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaioiTi4Gj5XLr","https://ap.wps.com/l/cbCaioiTi4Gj5XLr","pdf",45334,"English","# Average rates of change\n## Secant line equations\n## Critical thinking question","[{\"question\":\"How do you find the average rate of change over a given interval?\",\"answer\":\"Compute the change in the function output over the interval and divide by the corresponding change in the input values.\"},{\"question\":\"What is a secant line in these problems?\",\"answer\":\"The secant line is the straight line that intersects the function at two given points, and its equation is determined from those points.\"},{\"question\":\"Does the critical-thinking speed-limit question conclude the driver broke the limit?\",\"answer\":\"Yes. The provided reasoning states the average rate of change is 62 mph, implying the driver was breaking the speed limit some of the time.\"}]","Average Rates of Change - Worksheet | PDF",1791426198,10,{"code":4,"msg":82,"data":98},[99,103,107,110,115,120,125,130,135,138,141],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":100,"show_sort_weight":101,"slug":102},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":104,"show_sort_weight":105,"slug":106},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":108,"slug":109},70,"exam",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},5,"Comic",60,"comic",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},6,"Technology",50,"technology",{"id":121,"doc_module":4,"doc_module_name":25,"category_name":122,"show_sort_weight":123,"slug":124},7,"Healthcare",40,"healthcare",{"id":126,"doc_module":4,"doc_module_name":25,"category_name":127,"show_sort_weight":128,"slug":129},8,"Research & Report",30,"research-report",{"id":131,"doc_module":4,"doc_module_name":25,"category_name":132,"show_sort_weight":133,"slug":134},9,"Religion & Spirituality",20,"religion-spirituality",{"id":133,"doc_module":4,"doc_module_name":25,"category_name":136,"show_sort_weight":133,"slug":137},"World Cup","world-cup",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":139,"show_sort_weight":96,"slug":140},"Lifestyle","lifestyle",{"id":142,"doc_module":4,"doc_module_name":25,"category_name":143,"show_sort_weight":111,"slug":144},19,"General","general"]