Solving Quadratic Equations by Factoring PDF

ǫȄǐȐþçǥȎȐ ÖǔșìâǤǜÜǐǪȂȚǪȁòȢǒȌȚȎǰǖǔȐǐȑȁåÞǤǒ 2-2...

ǫȄǐȐþçǥȎȐ ÖǔșìâǤǜÜǐǪȂȚǪȁòȢǒȌȚȎǰǖǔȐǐȑȁåÞǤǒ 2-2 ǔȚǼȚǒǦǗȊâåȡêǐǼȎȊâȉǟ x ɮȉȍǐȈȊǐǒìâǤǝȊâȘǶǿǖüÞǤșǦǖþ ȉȍâȖǼȊâȗȊàȉȚȋǠǗȊǐǒ Solving Quadratic Equations x by Factoring 4 ft ǕțǽțǓǧǗǕȋêǑǽȎȊǠêǑǞȚà ĽǺȚǶǗǩÞ ȊȎâȗǽȋâȘȋàȊțȌǡǘȋǑǓ 6 ft îìǤȊâǦȚșǐǼȍ ȔdzǧǼþìâǥǞȋâúȗǶȊțǛȏǘȋȐȚìâǥȆȎǒǘȈâ.A 10.2.1 ć ȇǘǓǑǝàǟdzþÛȊȎǑȉȋǑǓìâǥǞȋâǕǠǑǫȎȊ Ǜć ȏȚĀǦȋâìâǥȆȏȋâǑȎ ǔȚȑǓȊâȉȎǼǗǩâ.B åǐǠȋǶǰȎȊâ ǕȋêǑǽȏȌȋǕțǪǑțȆȋâǕȀțDZȋâ ļ ÛìâǥǞȋâȐȎǥǽǓǕȑǑȒȃȋâȔƑǷȀǗȍȋĀǦȋâÜǨǞȋâǕǠǑǫȎǥȚǥǡǗȇȒȉȏȚȁțȈ.C ǕțǽțǓǧǘȋâ standardformofquadratic ÛǔȚǼȚǒǦǗȊâåȡêǐǼȎȊâȉǟȗȋǻȉȍâȖǼȊâȗȊàȉȚȋǠǗȊâùǤǻǐǪșȀȚȇ îǐǩȝâúâNjǪȊâ equation ĀǧȃDZȋâãǧǴȋâǜǗǑȑǕțǰǑǣ ļ ĀǦȂǰȊâãǦdzȊâǛǖǐȐǔȚǯǐǢúǐȎǼǗǩâ 1úǐǚȍ zero-product property  Û(x−9)( 5x+2)=0ǔȊêǐǼȎȊâȉǟêǐǝșàȆȑȈȎșȀȚȇ Öb þ a ǕțȆțȆǡȋâ êâǥǼȞâ ǻțȏǞȋ ȔȑÞ ȘȌǼ ĀǦȂǰȊâãǦdzȊâǛǖǐȐǔȚǯǐǢ ǯȒǗ b = 0 þÞ a = 0 ǑȎǍȂ Öab = 0 üǑȈ âëà Ȋǡȋâ êǑǞȚȠ ǕȋêǑǽȏȋâ șȂ ǧȃDZȋâ ĀþǑǫǗ șǘȋâ ȊȎâȗǽȋâ êćǥǠ åǐȄȢǼȊâȏǻǘǠǒâ (5x + 2) = 0 þÞ (x − 9) = 0 úǑȏǽǘǪǑǓ ǕȋêǑǽȏȋâ ýǦȕ ȊǠ șȂ ǧȉȂ 2 þǥǔǘǪ ȁțȈ șȑǑțǓ ȊțǛȏǗþ úþǥǝ x = − __ 5 ÖĀǧȃDZȋâ ãǧǴȋâ ǜǗǑȑ ǕțǰǑǤȋ ǑȆā Ȃþ x=9 ÛșȑǑțǓ ȊțǛȏǗ șȂþ Ûúþǥǝ șȂ úȗȌǡȋâ ÖǧȃDZȋâ ĀþǑǫȚ (x − 9) ǑȎà ǧȃDZȋâ ĀþǑǫȚ (5x + 2) þÞ ȐțȌǡȋâ ȣȈ ȐȎ ȄȆǡǗ 2 ñȗǼ x=−_ x = 9 ñȗć Ǽ 5 ć 2 __ 2 + 2) = 0 __ (9 − 9)(5(9) + 2) = 0 (− 5 − 9)(5(− 5) 2 __ (−9 5 )(0) = 0 (0)(47) = 0 0=0✓ 0=0✓ 2 þ x = 9 Ǒȏȕ üǑțȆțȆǠ üȣǠ (x − 9)(5x + 2) = 0 ǕȋêǑǽȏȌȋ Öüëà x=−_ 5 ǔȚȊǐǗȊâǔǠȂǰȊâȘȁǺǓǗș 45 ȊȎâȗǽȋâȘȋàȊțȌǡǘȋǑǓǕțǽțǓǧǘȋâåȢêǑǽȏȋâȊǠ 2-2îìǤȊâ M02_MTH03_SE10_QTR_AR_8973.indb 45 12/05/2022 6:14:16 PM  1úǐǚȎȊâǺǒǐǖ ȐțǘțȋǑǘȋâȐțǘȋêǑǽȏȋâȊǠą .1 ɭȉ ć ǠǖüÞúþǐǟ a. (2x − 1)(x + 3) = 0 b. (2x + 3)(3x − 1) = 0 ȉȍâȖǼȊâȗȊàȉȚȋǠǗȊǐǒǔȚǼȚǒǦǗȊâåȡêǐǼȎȊâȉǟ 2úǐǚȍ ȘȎȚȔǐȂȎȊâãǐǼȚǗǩȡâ Ûx2+9x=−20ǔȊêǐǼȎȊâȉǠȊȉȍâȖǼȊâȗȊàȉȚȋǠǗȊâúǐȎǼǗǩâȆȑȈȎșȀȚȇ ɯa ≠ 0 ǙțǠ Öax 2 + bx + c = 0 șȕ ǔȚǼȚǒǦǗȊâǔȊêǐǼȎȋȊǔȚǩǐȚȅȊâǔǿȚǰȊâ ǕțǪǑțȆȋâǕȀțDZȋâșȂǕȋêǑǽȏȋâǒǘȈâ 1 äȖǶǣȊâ x 2 + 9x = −20 úǑȏǽǘǪǑǓǕțǽțǓǧǗǕȋêǑǽȎȊǠǥȒǼ Ǒȏā ǏâêÞǥǓâÖȊȎâȗǽȋâȘȋàȊțȌǡǘȋâ x 2 + 9x + 20 = 0 ǕțǪǑțȆȋâǕȀțDZȋâșȂǕȋêǑǽȏȋâǕǓǑǘȉǓ ǕǼȗȏǞȎ úǑȏǽǘǪâ ȐȉȏȚ Öx 2 + 9x + 20 = 0 Ȋǡȋ ȊȎâȗǽȋâ ǕǼȗȏǞȎ êǑǞȚȠ Ȣþǥǝ ā ǎǮȑÞ 2 äȖǶǣȊâ ǕȋêǑǽȏȋâ Ȋǡȋ 9 ǑȖǼȗȏǞȎþ 20 ǑȖǓǧdz ǜǗǑȑ șǘȋâ ȊȎâȗǽȋâ 20êǥǽȋâȊȎâȗǼ ȊȎâȗǽȋâôȗȏǞȎ 1 , 20 21 ĀþǑǫȚ 5 þ 4 ȐțȌȎǑǽȋâ ãǧdz ǜǗǑȑ 2 , 10 12 4,5 9 ɯ9 ĀþǑǫȚ ǑȏȖǼȗȏǞȎþ 20 ǕțȌțȌǡǘȋâ ǕȀțDZȋâ șȂ ǕȋêǑǽȏȌȋ ǕțǪǑțȆȋâ ǕȀțDZȋâ ǕǓǑǘȈ ǥǼÞ 3 äȖǶǣȊâ ǔȚǩâìêǔǠȚǰȐ ǕȀțDZȋâ ȊțȌǡǗ ȇȑǑȉȎǍǓ üǑȈ âëà (x + 4)(x + 5) = 0 ȔȑǍȂ ÖȊȎâȗǽȋâ Șȋà ǕȋêǑǽȏȌȋ ǕțǪǑțȆȋâ Ȋǡȋâ êǑǞȚà ȇȒȉȏȚ ǕȋêǑǽȏȋâ Ȋǡȋ ĀǧȃDZȋâ ãǧǴȋâ ǜǗǑȑ ǕțǰǑǣ ȊȏǽǘǪâ 4 äȖǶǣȊâ (x + 4) = 0 þÞ (x + 5) = 0 x = −4 x = −5 x = −5 þ x = −4 Ǒȏȕ üǑțȆțȆǠ üȣǠ x 2 + 9x + 20 = 0 ǕȋêǑǽȏȌȋ Öüëà ȊȎâȗǽȋâȘȋàȊțȌǡǘȋǑǓȐțǘțȋǑǘȋâȐțǘȋêǑǽȏȋâ ȊǠą .2 ɭȉ ć ǠǖüÞúþǐǟ a. x 2 + 16x + 64 = 0 b. x 2 − 12x = 64 ǕțǽțǓǧǘȋâåǑȒȚǑǔǘȏȋâþåȢêǑǽȏȋâ 2äǤǟȖȊâ 46 M02_MTH03_SE10_QTR_AR_8973.indb 46 12/05/2022 6:14:16 PM  äǐȚǠȊâǺȄâþȏȍȉǎǐǪȍȉǠȊȉȍâȖǼȊâȗȊàȉȚȋǠǗȊâúǐȎǼǗǩâ 3úǐǚȍ ȃȚǓǶǖ ft ɮxǽȋǓșǤǟȖȍñǦǼǒȘǜìǐǢĀëȡȖȁǴǎǐǟȓȊȀǠǗȍȖǓȄ 20 x 1664ft2ȘǜìǐǣȊâĀëȡȖȂȊâǴǎǐǠȊâǺȍȖǓȅȊâȀȅǩǔǟǐǪȍǽȋǓǖ 40 ft ɮȘǜìǐǣȊâĀëȡȖȂȊâǴǎǐǠȊâñǦǻǤǜþÞ ȗǔȆȋâ ǕǠǑǫȎ ȊțǛȏǘȋ ǕȋêǑǽȎ ǒǘȈâ ǽǯą (2x + 20)(2x + 40) = 1 664 ñǧǽȋâ × úȗǷȋâ = ǕǠǑǫȏȋâ ǕțǪǑțȆȋâ ǕȀțDZȋâ șȂ ǕȋêǑǽȏȋâ ǒǘȈâ ǻȚíȗǘȋâ ǕțǰǑǣ ȊȏǽǘǪâ ǑǪǟâ (2x + 20)(2x + 40) = 1 664 4x 2 + 120x − 864 = 0 4x 2 + ____ ___ 120x 864 0 ȘȌǼ ǥǠ ȊȈ ȍǫȅâ 4 4 − ___ 4 = __ 4 ǕȋêǑǽȏȋâ ǵțǫǔǘȋ 4 x 2 + 30x − 216 = 0 (x − 6)(x + 36) = 0 ć Öüëà x = −36 þ x = 6 Ǒȏȕ ǕȋêǑǽȏȋâ ȣǠ ǦǪȁ ć 6 ft ȗȕ ǵǏǑǡȋâ ñǧǼ ÖüëàȊǡȋâ ȗȕ −36 üȗȉȚ üÞ ȐȉȏȚ Ȣ âǦȋ Ǒǔā ȋǑǪ ǵǏǑǡȋâ úȗǶ üȗȉȚ üÞ ȐȉȏȚ Ȣ Ȋǡȋâ ȐȎ ȄȆǡǗ ǕțȌǰȞâ ǕȋêǑǽȏȋâ șȂ x = 6 ñȗć Ǽ [2(6) + 20] [2(6) + 40] = 1 664 (32)(52) = 1 664 ✓ ÛìǑǶȠâñǧǼǑȎÖ504 cm 2 ĀþǑǫǗ ìǑǶà Ȋǣâê äìȗǰ ǕǠǑǫȎ.3 ɭȉ ć ǠǖüÞúþǐǟ x x 30 cm 504 cm2 20 cm 47 ȊȎâȗǽȋâȘȋàȊțȌǡǘȋǑǓǕțǽțǓǧǘȋâåȢêǑǽȏȋâȊǠ 2-2îìǤȊâ M02_MTH03_SE10_QTR_AR_8973.indb 47 12/05/2022 6:14:17 PM  ǐȚāć ȐǐȚǒǔȚǼȚǒǦǖǔȊâêȉȚǚȎǗȊǔȚȋȚȋǠǗȊâǔǿȚǰȊâúǐȎǼǗǩâ 4úǐǚȍ ÛǐȚāć ȐǐȚǒf(x)=x2−2x−8ǔȊâǤȊâȉȚǚȎǗȊȉȍâȖǼȊâȗȊàȉȚȋǠǗȊâúǐȎǼǗǩâȆȑȈȎșȀȚȇ ć ȊȎâȗǽȋâȘȋàǕțǽțǓǧǘȋâǕȋâǥȋǑǓǕǷǔǗǧȏȋâǕțǽțǓǧǘȋâǕȋêǑǽȏȋâȊȌǠ 1 äȖǶǣȊâ x 2 − 2x − 8 = 0 (x + 2)(x − 4) = 0 ǕȋêǑǽȏȋâ úȗȌǠ êćǥǠ 2 äȖǶǣȊâ (x − 4) = 0 þÞ (x + 2) = 0 x=4 x = −2 Ö−2 þ 4 Ǒȏȕþ x ȐțǽǷȆȏȋâ ǵǪȗǘȎ ǥǝþÞ îÞǧȋâ åǑțǚâǥǠà ǥǝþÞ 3 äȖǶǣȊâ ǔȚǩâìêǔǠȚǰȐ 4 + (−2) _______ ǻȆȚ ȇȋǦȋ ÖǧǹǑȒǘȎ ǎȂǑȉȏȋâ ǻǷȆȋâ =1 2 ȐțǽǷȆȏȋâ ȐțǓ ȁDZǘȒȏȋâ șȂ îÞǧȋâ 1 ȗȕ îÞǧȌȋ x șǚâǥǠȠâ șȂ x șǚâǥǠȠâ ñȗć Ǽ ɯx ìȗǡȏȋâ ȐȎ îÞǧȌȋ y șǚâǥǠȠâ ǥǝþÞ ǕțǽțǓǧǘȋâ Ǖȋâǥȋâ f(1) = (1) 2 − 2(1) − 8 = −9 (1 , −9) șȕ îÞǧȋâ åǑțǚâǥǠà Öüëà y x -4 O 2 ɯx ìȗǡȏȋâ ȐȎ ȐțǽǷȆȏȋâþ îÞǧȋâ ȊǛć Ȏ 4 äȖǶǣȊâ -4 ȍǪǧȋ x ìȗǡȏȋâ ȐȎ ȐțǽǷȆȏȋâþ îÞǧȋâ ȊȏǽǘǪâ -8 șȑǑțǔȋâ ȊțǛȏǘȋâ Ǒāțć ȑǑțǓ f(x) = 2x 2 + 5x − 3 Ǖȋâǥȋâ ȊțǛȏǘȋ ȊȎâȗǽȋâ Șȋà ȊțȌǡǘȋâ ȊȏǽǘǪâ.4 ɭȉ ć ǠǖüÞúþǐǟ ǔȚǼȚǒǦǖǔȊâǤȊǔȚȋȚȋǠǗȊâǔǿȚǰȊâǔǒǐǗȇ 5úǐǚȍ ÛýǐȐêÞȘȐǐȚǓȊâȉȚǚȎǗȊǐǒǔǶǓǖǦȎȊâǔȚǼȚǒǦǗȊâǔȊâǤȋȊǔȚȋȚȋǠǗȊâǔǿȚǰȊâǔǒǐǗȇȆȑȈȎșȀȚȇ y x -6 -4 -2 O 2 (−5 , 0) -2 -4 (1 , 0) -6 -8 (−2 , −9) ǔȚȊǐǗȊâǔǠȂǰȊâȘȁǺǓǗș ǕțǽțǓǧǘȋâåǑȒȚǑǔǘȏȋâþåȢêǑǽȏȋâ 2äǤǟȖȊâ 48 M02_MTH03_SE10_QTR_AR_8973.indb 48 12/05/2022 6:14:18 PM  5úǐǚȎȊâǺǒǐǖ x ȐțǽǷȆȏȋâ ǥǝþÞ 1 äȖǶǣȊâ 1 þ −5 Ǒȏȕ x üǑǽǷȆȏȋâ ǕțȌțȌǡǘȋâ ǕȀțDZȋâ șȂ ǕțǽțǓǧǘȋâ ǕȋêǑǽȏȋâ ǒǘȈâ 2 äȖǶǣȊâ ǑȖȌȎâȗǽȋ ȐțȌǠ ǑȏȖȑȞ ǕțǽțǓǧǘȋâ ǕȋêǑǽȏȌȋ ȐțȌǠ üȣǛć ȏȚ ȐȚǦȌȋâ Öx ȐțǽǷȆȏȋâ ȊȏǽǘǪâ ǔȚǩâìêǔǠȚǰȐ a(x − p)(x − q) = 0 ǕǐȂǑȉȏȋâ ôȗǷȆȋâ ȐȎ șǏǑȖȑȢ êǥǼ ǧȏȚ a[x − (−5)] [x − (1)] = 0 q þ p șǘȏțȆǓ x ȐțǽǷȆȏȋâ ȐǼ ñȗć Ǽ âǦȋ (1 , 0) þ (−5 , 0) ȐțǘǷȆȒȋǑǓ êǑǞȚȠ a Ǖȏțȅ ǥȚǥǡǗ ȇțȌǼ ǒǞȚ a(x + 5)(x − 1) = 0 ā ǧȏȚ ĀǦȋâ ǥțǠȗȋâ ǎȂǑȉȏȋâ ǻǷȆȋâ ǑǴȚÞ ǕțȌțȌǡǘȋâ ǕȀțDZȋâ șȂ Ǖȋâǥȋâ ǒǘȈâ 3 äȖǶǣȊâ (−2 , −9) ǕǷȆȒȋǑǓ a Ǖȏțȅ êǑǞȚȠ ǕǛȋǑǚ ǕǷȆȑ ȊȏǽǘǪâ f(x) = a(x + 5) (x − 1) îÞǧȋâ ȊȏǽǘǪâ −9 = a(−2 + 5)(−2 − 1) ɯf(–2) = –9 þ x = –2 ñȗć Ǽ a=1 f(x) = (x + 5) (x − 1) þÞ f(x) = 1(x + 5)(x − 1) șȕ ǕțǽțǓǧǘȋâ ǕȋâǥȌȋ ǕțȌțȌǡǘȋâ ǕȀțDZȋâ Öüëà Û ýǑȑêÞ Ǒāțć ȑǑțǓ ǕȌǛȏȏȋâ ǕȋâǥȌȋ ǕțȌțȌǡǘȋâ ǕȀțDZȋâ ǑȎ.5 ɭȉ ć ǠǖüÞúþǐǟ y 2 x O 2 4 6 8 10 -2 -4 -6 -8 49 ȊȎâȗǽȋâȘȋàȊțȌǡǘȋǑǓǕțǽțǓǧǘȋâåȢêǑǽȏȋâȊǠ 2-2îìǤȊâ M02_MTH03_SE10_QTR_AR_8973.indb 49 12/05/2022 6:14:19 PM  ȉȍâȖǼȊâȗȊàȉȚȋǠǗȊǐǒǔȚǼȚǒǦǗȊâåȡêǐǼȎȊâȉǟ ûȖȕȂȎȊâǮǣȋȍ Öb þ a ǕțȆțȆǡȋâ êâǥǼȞâ ǻțȏǞȋ ȔȑÞ ȘȌǼ ĀǦȂǰȊâãǦdzȊâǛǖǐȐ ǕțǰǑǣ ǯȒǗ ǐȚāć ǹȂȊ ǕȀțDZȋâ șȂ ǕțǽțǓǧǗ ǕȋêǑǽȎ ȘȌǼ ĀǧȃDZȋâ ãǧǴȋâ ǜǗǑȑ ǕțǰǑǣ ȄțǔǷǗ ȇȒȉȏȚ b = 0 þÞ a = 0 ǑȎǍȂ Öab = 0 üǑȈ âëà ǕțǽțǓǧǘȋâ ǕȋêǑǽȏȋǑǓ ǕǷǔǗǧȏȋâ ǕȋâǥȌȋ șȑǑțǔȋâ ȊțǛȏǘȌȋ x ȐțǽǷȆȏȋâ êǑǞȚȠ ǕțȌțȌǡǘȋâ x 2 + 2x − 3 = 5 x 2 + 2x − 8 = 0 ǐāćșǦǓǜ ǕȀțDZȋâ șȂ ǕȋêǑǽȏȋâ ǒǘȈâ (x + 4) (x − 2) = 0 ȊȎâȗǽȋâ Șȋà ǑȖȌȌǠþ ǕțǪǑțȆȋâ (x − 2) = 0 þÞ (x + 4) = 0 x=2 x = −4 x = 2 þ x = −4 Ǒȏȕ üǑțȆțȆǠ üȣǠ ǕțǽțǓǧǘȋâ ǕȋêǑǽȏȌȋ y f(x) = x 2 + 2x – 8 ǐȚāć ȐǐȚǒ 8 4 x -4 -2 O 2 4 x üǑǽǷȆȏȋâ -4 ȊțǛȏǘȌȋ x üǑǽǷȆȏȋâ ȄǓǑǷǘȚ 2 þ −4 Ǒȏȕ -8 Ǖȋâǥȋâ ìǑȃǰÞ ǻȎ șȑǑțǔȋâ ȆȎȕȁȃǓć ǵ ȆȎȕȁȏǻǦǓć ǻ ɫȘȋșǐȎȍǔȊêǐǼȍȉȇȉ ąǟÖ6þ5ȏȚȑșǦȎǗȊâȘȁ ȊȎâȗǽȋâȘȋàȊțȌǡǘȋâùǥǼǑǫȚȁțȈ îǐǩȝâúâNjǪȊâ â.1 5. (x − 10)(x + 20) = 0 6. (3x + 4)(x − 4) = 0 ÛǕțǽțǓǧǘȋâåȢêǑǽȏȋâȊǠȘȌǼ ɮȉȍâȖǼȊâȗȊàȉȚȋǠǗȊǐǒȘȋșǐȎȍǔȊêǐǼȍȉȇȉ ąǟÖ8þ7ȏȚȑșǦȎǗȊâȘȁ ȐțǘȋêǑǽȏȋâúȗȌǠȐțǓüìǑȅ ǔȚȑǓȊâȉȎǼǗǩâ.2 7. x 2 + 18x + 32 = 0 8. x 2 − 4x − 21 = 0 4x2+10x−14=0þ2x2+5x−7=0 ć ȇǘǓǑǝàǟdzþÛǸǠȣǗâëǑȎ ɫȘȋșǐȎȍǔȊêǐǼȍȉȇȉ ąǟÖ12-9ȏșìǐȎǗȊâȘȁ ȘǘȎÛĀǧȃDZȋâãǧǴȋâǜǗǑȑǕțǰǑǣșȕǑȎ åǐǠȋǶǰȎȊâ.3 9. x 2 + 2x = −1 10. x 2 − 8x = 9 ć ȇǘǓǑǝàǟdzþÛǕțǽțǓǧǗǕȋêǑǽȎȊǡȋǑȖȋǑȏǽǘǪâȇȒȉȏȚ 11. 2x 2 + x = 15 12. 5x 2 − 19x = −18 ā ǕȏțȅȣȎǑȈǑ ǽǓǧȎȊȉǮǗșǘȋâêþǥǡȋâǕțǚȣǛȋǖȑǑȈâëà ā ć.4 ȌȎǻ y ǕȀțDZȋâșȂÖǕțǽțǓǧǗǕȋêǑǽȎǒǘȈâ.13 ć ȇǘǓǑǝàǟdzþÛǕȋêǑǽȏȌȋ ā ć ȣǠȍȉȂÖǧȃDZȋâĀþǑǫǗ 16 ǻȎǑȖȋȗȌǠȄǓǑǷǘǗÖǕțȌțȌǡǘȋâ 8 ǕțǽțǓǧǘȋâǕȋâǥȌȋxȐțǽǷȆȏȋâ x ìþǑǞȏȋâȊȉǮȋâșȂǑāțć ȑǑțǓǕȌǛƏ ȏȏȋâ -8 -4 O 4 8 -8 ć.14 ǕȋêǑǽȏȋâȊȌǠ -16 ȊȎâȗǽȋâȘȋàx2−6x+5=0 ȊǛć ȎȍǚÖǕțǽțǓǧǘȋâǕȋêǑǽȏȋǑǓǕǷǔǗǧȏȋâǕȋâǥȌȋîÞǧȋâåǑțǚâǥǠàǥǝþÞ Ǒāțć ȑǑțǓf( x)=x2−6x+5Ǖȋâǥȋâ ǕțǽțǓǧǘȋâåǑȒȚǑǔǘȏȋâþåȢêǑǽȏȋâ 2äǤǟȖȊâ 50 M02_MTH03_SE10_QTR_AR_8973.indb 50 12/05/2022 6:14:20 PM  ȉǎǐǪȍȉǟþã ą ìƏ Ǥǖ ãìƏ Ǥǖ ȆȎȕȁíćǧǻ 1úǐǚȎȊâǦǹȐâ ɮȘȋșǐȎȍǔȊêǐǼȍȉȇȉ ąǟÖ23-20ȏșìǐȎǗȊâȘȁ ĀǦȋâǑȎÖ8ȗȕǕțǽțǓǧǗǕȋêǑǽȎúȗȌǠǥǠÞüǑȈâëà ǐȚāć ȅǶȑȍìǦć ǒ.15 ȇȒȉȏȚüǑǘȌȋâüǑǘȆȚǧǷȋâǑȎÛǕțǽțǓǧǘȋâǕȋêǑǽȏȋâȐǼȔǘȂǧǽȎȇȒȉȏȚ 20. (x − 5)(x + 2) = 0 21. (2x − 5)(7x + 2) = 0 āć ÛǕțǽțǓǧǘȋâǕȋêǑǽȏȌȋȣǠȗȕȊǡȋââǦȕüǑȈâëàǑȎǕȂǧǽȎǑȏȖȋȣǣȐȎ 22. 3(x + 2)(x − 2) = 0 23. (3x − 8) 2 = 0 șȌȚǑȏȎǕȋǑǠȊȉȋǕțǽțǓǧǗǕȋêǑǽȎǒǘȈâ ǔȄǤǒȉǯâȖǖ.16  ɮȉȍâȖǼȊâȗȊàȉȚȋǠǗȊǐǒǔȊêǐǼȍȉȇȉ ąǟÖ29-24ȏșìǐȎǗȊâȘȁ șȆǷȒȏȋâùǧȚǧǔǗèǧǭâ 3þ2ȏȚȊǐǚȎȊâǦǹȐâ ǧǣȜâ îȗȉǽȎ ǑȏȕǥǠÞ üȣǠ ǕȋêǑǽȏȌȋ.a 24. x2 + 2x + 1 = 0 25. x2 − 5x − 14 = 0 ǥǠâþ ȊǠ ǕȋêǑǽȏȌȋ.b 26. x 2 + 7x = 0 27. 2x 2 − 5x + 2 = 0 ȊȎâȗǽȋâȘȋàǕȋêǑǽȏȋâȊțȌǡǗșȂǒȋǑǷȋâNjǷǣȐțć Ǔ NJǶǣȊâȉćȋǟ.17 28. 2x 2 + 3x = 5 29. 5x 2 + 16x = −3 Ȕǡǡǰþ ǔȅǶȑȎȊâǔǟǐǪȍȉȚǚȎǗȊǔȊêǐǼȍǑǗȇâÖ31þ30ȏȚȑșǦȎǗȊâȘȁ x2 + 2x Ũ 3 = 5 3úǐǚȎȊâǦǹȐâ ɮxǔȎȚȄǤǜþÞȌǙÖǔȋȋǹȎȊâ (x Ũ 1)(x + 3) = 5 198cm2ǕțȌȉȋâǕǠǑǫȏȋâ.30 x Ũ 1 = 5 þÞ x + 3 = 5 x = 6 þÞ x = 2 x 9 cm ǕȋêǑǽȏȋâȊȌǡǗȁțȈèǧǭâ ȉǠȊâȘȁǦǒǐǙþǦȈć ȁ.18 16 cm ǑȖȌȎâȗǼȘȋà2x2+8x+  6=0 x üǑțȑǑțǓüȣțǛȏǗǑȏȕýǑȑêÞüǑǐȂǑȉȏȋâüǑǽǷȆȋâ ǐȚȋǼȊâǦȚȈȂǗȊâåâìǐȕȍ.19 24 in.31 ȐțǘțǽțǓǧǗȐțǘȋâǥȋ x y x 12 in 189 in² = ǕțȌǣâǥȋâǕǠǑǫƯâ 12 4 ÖȉȍâȖǼȊâȗȊàǔȊêǐǼȎȊǐǒǔǶǓǖǦȎȊâǔȊâǤȊâȉȋǟÖ33þ32ȏȚȑșǦȎǗȊâȘȁ x O 2 4 6 8 4úǐǚȎȊâǦǹȐâ ɮǐȚāć ȐǐȚǒǔȊâǤȊâȉǚć ȍȌǙîÞǦȊâåǐȚǙâǤǟàǤǜþÞþ -4 32. x2 − 2x − 63 = 0 33. x2 + 16x + 63 = 0 5úǐǚȎȊâǦǹȐâ ɮǔȚǼȚǒǦǗȊâǔȊâǤȋȊǔȚȋȚȋǠǗȊâǔǿȚǰȊâǑǗȇâ Ȑțǘȋâǥȋâ ÿǥǠǍǓ ǕǷǔǗǧȏȋâ ǕȋêǑǽȏȌȋ ǕțȌțȌǡǘȋâ ǕȀțDZȋâ ǒǘȈâ.a Û ǑȖǘǔǘȈ șǘȋâ Ǖȋâǥȋâ ȊǛć ȏȚ ȘȒǡȒȎ ĀÞ y .34 12 ā ÿǧǣȞâ ǕȋâǥȋǑǓ ǕǷǔǗǧȏȋâ ǕȋêǑǽȏȋâ êǑǞȚȠ ǑāǘǓǑǚ ȣȎǑǼ ȊȏǽǘǪâ.b 6 ǕȅȣǽȋâýǦȕǟǴǘǗȁțȈÛȐțǘȋâǥȋâȐțǓǑȖǺǠȣǗșǘȋâǕȅȣǽȋâǑȎ.c x ÛǖǓǑǛȋâúȣǣȐȎ -4 -2 O 2 4 -6 -12 51 ȊȎâȗǽȋâȘȋàȊțȌǡǘȋǑǓǕțǽțǓǧǘȋâåȢêǑǽȏȋâȊǠ 2-2îìǤȊâ M02_MTH03_SE10_QTR_AR_8973.indb 51 12/05/2022 6:14:21 PM  ȉǎǐǪȍȉǟþã ą ìƏ Ǥǖ ìǐǓǗǢâȗȋǻãìƏ Ǥǖ ȃǓć ǵ ǕțǪǑțȆȋâǑȖǘȀțǰȊȎâȗǼȐȎǧǛȈÞþÞȊȎǑǽǓǕȋêǑǽȎȊȈȊǰĆ.37 äǥȏǓȔȌțǘȂúǑǽǭàǥǽǓüȗȌȎǵȚǧǭȄȌǶąÞ åǐȚDzǐșǦȊâȘȁǴǒâþì.35 I. x 2 + 6x = −8 A. 2x − 3 ȔȋǑǽǭàȐȎ8 sǥǽǓñìȞâȘȋàǵǔȕþ3s y II. 2x 2 + x = 6 100 B. x + 4 80 III. x 2 + 2x = 8 C. x − 4 ôǑȃǗìȢâ 60 IV. 2x 2 + 5x = 12 D. x + 2 (ft) 40 V. 2x 2 − 11x = −12 E. x − 2 20 ǕțǽțǓǧǗǕȋêǑǽȎúȗȌǠǥǠÞ SAT/ACTìǐǓǗǢâ.38 x ǕțǽțǓǧǘȋâǕȋâǥȋâîÞìǻȆȚþ−2ȗȕx2+  bx+  c=0äìȗDZȋâșȂ 0 2 4 6 8 10 ÛǕȋêǑǽȏȌȋǧǣȜâȊǡȋâǑȎɯ( 2ɯ5,−20ɯ25)ǥȒǼǑȖǓǕǷǔǗǧȏȋâ (s) ȐȎǨȋâ 𝖠 −11 ǕȀțDZȋâ șȂ ǕȋǑǡȋâ ýǦȕ çǦȏȒǗ șǘȋâ ǕțǽțǓǧǘȋâ ǕȋêǑǽȏȋâ ǑȎ.a 𝖡 −4.5 Û ǕțȌțȌǡǘȋâ șǘȋâ ǕȋêǑǽȏȋǑǓ ǕǷǔǗǧȏȋâ ǕȋâǥȌȋ îÞǧȋâ ǕǷȆȑ åǑțǚâǥǠà ǑȎ.b 𝖢 0.5 þ Ǖȋâǥȋâ ýǦȖȋ îÞǧȋâ ǕǷȆȑ ȐțǓ ǕȑìǑȆȏȋâ Ȕǝþ ǑȎ Û ǑȖǗǥǝþÞ 𝖣7 Û ýȣǼÞ șȑǑțǔȋâ ȊțǛȏǘȌȋ îÞǧȋâ ǕǷȆȑ 𝖤9 șǘȋâ ǕȋâǥȌȋ ǕțȌțȌǡǘȋâ ǕȀțDZȋâ șȂ ȔǓǧdz ȇȒȉȏȚ ĀǦȋâ ǖǓǑǛȋâ ǑȎ.c ć ÛýȣǼÞ șȑǑțǔȋâ ȊțǛȏǘȋâ Ǖȋâê ȘȌǼ ȊDZǡǘȋ ǑȖǘǔǘȈ ȇǘǓǑǝà ǟdzþ ǕȈǧǓǕȂǑǠȐǼ1ftǥǽǔǗäìȗȂǑȑîǥȒȖȎȍȏDZȚ ǔȚǎâêÞǔȎȕȍ.39 ǕȈǧǓǨȈǧȎșȂäìȗȂǑȒȋâýǑțȎǵȆǫǗǙțǡǓ10ftǑȖdzǧǼǕǠǑǔǪ ȘȌǼÞ÷ǑǷǤǓǖǔǛȎ15ftȔȋȗǶșȑǥǽȎȇȌǪ ǔȚȑǓȊâȉȎǼǗǩâ.36 ǎȂǑȉȎǻǷȅȊȉǭȘȌǼäìȗȂǑȒȋâȐȎǕǷȅǑǫȋâýǑțȏȋâìǑǫȎǕǠǑǔǫȋâ êȗȏǽȋâäǥǼǑȅȘȋà÷ǑǷǤȋâȐȎǕȂǑǫȏȋâûȗȌǽȎǧțǿȔǼǑȃǗìâêȗȏǼ 3ftìâǥȆȏǓêȗȏǽȋâôǑȃǗìâȐȎǧDZȅÞ 1 ft 10 ft 15 x ft ft ɯäìȗȂǑȒȋâȐȎÜǑȏȋâȄȂǥǗǻȅȗȎ(1,0)ǕǷȆȒȋâȐȉǘȋ AÜǧǝȊâ ɯýǑțȏȋâìǑǫȎǕǝǦȏȒȋǕțǽțǓǧǗǕȋêǑǽȎǒǘȈâ (x – 3) ft ÛäìȗȂǑȒȋâȐȎȄȂǥǘȏȋâÜǑȏȌȋôǑȃǗìâȘDZȅÞǑȎ BÜǧǝȊâ ɯAÜǨǞȋâȐȎȇǘȋêǑǽȎȊȏǽǘǪâ Û êȗȏǽȋâ ôǑȃǗìâ êǑǞȚȠ ȊȏǽǘǫǗ üÞ ȇȒȉȏȚ âëǑȎ.a ȘDZȅÞüǑȈâëàäìȗȂǑȒȋâȐȎȄȂǥǘȏȋâÜǑȏȋâìǑǫȎǕȋêǑǽȎǑȎ CÜǧǝȊâ ą êȗȏǽȋâ ôǑȃǗìâ êǑǞȚȠ ǕțǽțǓǧǗ ǕȋêǑǽȎ ǒǘȈâ.b ǑȖȌǠþ Û4ftüȗȉȚüÞǒǞȚÜǑȏȌȋôǑȃǗìâ ÛêȗȏǽȋâäǥǼǑȅȐǼ÷ǑǷǤȋâǥǽǔȚȍȈ.c ǕțǽțǓǧǘȋâåǑȒȚǑǔǘȏȋâþåȢêǑǽȏȋâ 2äǤǟȖȊâ 52 M02_MTH03_SE10_QTR_AR_8973.indb 52 12/05/2022 6:14:22 PM