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Unit 1-Lesson 3

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School
St Edmund Campion Secondary School**We aren't endorsed by this school
Course
MATH MCR3UP
Subject
Mathematics
Date
Dec 16, 2024
Pages
34
Uploaded by Nefth
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\hh@uLE<£{°£{°zR‡rrJ ʹˁ ʂʷˍʹ ppH}±¥Ú zR‡ ppH}VTTarrJ zR‡\S ± ±C3 ±«ƒ¸VTTa= \S rrJ=«ƒ¸VTTazR‡rrJ+or vertex form´you are required tofill in the values forh³ k and a¶Step ´±9o find the‘a’value select onepoint that lies on thegraph µthe y·int¶²¸³ ¹±
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hh@uLE<£{°£{°zR‡rrJ ʹˁ ʂʷˍʹ ppH}±¥Ú zR‡ ppH}VTTarrJ zR‡\S ± ±C3 ±«ƒ¸VTTa= \S rrJ=«ƒ¸VTTazR‡rrJStep »±:seELIMINATIONto determine the values of ‘a’ and ‘b’³a = ° º b = µ
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hh@uLE<£{°£{°zR‡rrJ ʹˁ ʂʷˍʹ ppH}±¥Ú zR‡ ppH}VTTarrJ zR‡\S ± ±C3 ±«ƒ¸VTTa= \S rrJ=«ƒ¸VTTazR‡rrJSECTION ´!: Completing The Square
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hh@uLE<£{°£{°zR‡rrJ ʹˁ ʂʷˍʹ ppH}±¥Ú zR‡ ppH}VTTarrJ zR‡\S ± ±C3 ±«ƒ¸VTTa= \S rrJ=«ƒ¸VTTazR‡rrJSECTION ´!: Completing The Square(&3 >4: 2&0* 9-*8* 5*7+*(9 86:&7* 97.342.&18$9o find the last term in aperfect square trinomialuse the rule# the last termof a perfect squaretrinomial ishalf of themiddle term squared¶
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hh@uLE<£{°£{°zR‡rrJ ʹˁ ʂʷˍʹ ppH}±¥Ú zR‡ ppH}VTTarrJ zR‡\S ± ±C3 ±«ƒ¸VTTa= \S rrJ=«ƒ¸VTTazR‡rrJSECTION ´!: Completing The Square9here are many ways to find themax or minof aquadratic function³ 9he two methods taught in thislesson are#°¶completing the square´¶partial factoring<e will look at each method in detail³
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hh@uLE<£{°£{°zR‡rrJ ʹˁ ʂʷˍʹ ppH}±¥Ú zR‡ ppH}VTTarrJ zR‡\S ± ±C3 ±«ƒ¸VTTa= \S rrJ=«ƒ¸VTTazR‡rrJSECTION ´!: Completing The Square
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hh@uLE<£{°£{°zR‡rrJ ʹˁ ʂʷˍʹ ppH}±¥Ú zR‡ ppH}VTTarrJ zR‡\S ± ±C3 ±«ƒ¸VTTa= \S rrJ=«ƒ¸VTTazR‡rrJ(onvert the following equation intovertex formbycompleting the square¶
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hh@uLE<£{°£{°zR‡rrJ ʹˁ ʂʷˍʹ ppH}±¥Ú zR‡ ppH}VTTarrJ zR‡\S ± ±C3 ±«ƒ¸VTTa= \S rrJ=«ƒ¸VTTazR‡rrJSECTION ´!: Completing The Square<hat is thevertexand theaxis of symmetryof theparabola$ .s the vertex amax or minpoint$;ertex#²h³ k±→·½´ º"¸ &³4³8³ #x = h→ x & ½9he vertex is amaximum pointbecause theparabolaopens down ²a䠘¸±³
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Total Profit = ²profit per scarf±²number of scarves sold±hh@uLE<£{°£{°zR‡rrJ ʹˁ ʂʷˍʹ ppH}±¥Ú zR‡ ppH}VTTarrJ zR‡\S ± ±C3 ±«ƒ¸VTTa= \S rrJ=«ƒ¸VTTazR‡rrJAPPLICATION PROBLEM!:2aximizing 5rofit9wo high school students areknitting scarves to sell at the craftshow to raise money for the animalshelters in their community³9hefabricfor each scarfcosts ¿À9hey wereplanning tosellthe scarves for¿°¸each´ the same as last year whenthey sold»¸ scarves³ -owever´ theyknow that if they raise the price´ theywill make more profit´ even if theyend up selling fewer scarves³9heyhave been told that for every¼¸cent increasein the price´ they canexpect tosell four fewer scarves¶What selling price will maximize theirprofit and what will the profit be?Step°# +ind an equation to modeltheir total profit°1etxrepresent the number of ³¼¸ increasesÁRemember# in the first bracket . substituted allthe values aboutmoney and in the secondbracket . substituted all the values aboutquantity³ 9hen . usedFOILto expand and simplify³
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hh@uLE<£{°£{°zR‡rrJ ʹˁ ʂʷˍʹ ppH}±¥Ú zR‡ ppH}VTTarrJ zR‡\S ± ±C3 ±«ƒ¸VTTa= \S rrJ=«ƒ¸VTTazR‡rrJAPPLICATION PROBLEM!:2aximizing 5rofitStep ´# +ind the max value of the function by eithercompleting the squareor by using partial factoring³Vertex ²°³ °À´±x = °represents the number of ³»¾increasesy = °À´represents the maximum profit
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hh@uLE<£{°£{°zR‡rrJ ʹˁ ʂʷˍʹ ppH}±¥Ú zR‡ ppH}VTTarrJ zR‡\S ± ±C3 ±«ƒ¸VTTa= \S rrJ=«ƒ¸VTTazR‡rrJAPPLICATION PROBLEM!:2aximizing 5rofit<hatselling pricewill maximize their profitand what will theprofitbe$V±²³ ²!6´µx = ² represents the number of ° 5¶ increasesy = ²!6´ represents their profitHow do we find theselling price that will givethe maximum profit?±°² ³ ´µ² $"$ ±°²´µ²
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