9.12 Quadratics Review

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1 Algebra Name _ B2g0gD6L jkwudtaaa msvopfwtowiarneq CLOLXCa.I K `Awljla `rtiugohhtfs_ QrIefsfeYrZvtetdf. 9.2 Quadratics Review ) What is the difference between the two mathematical statements below? Then please eplain how ou could simplif or solve each one. Date Alg = 0 2) What does it mean to solve an equation? How can ou check if a solve is correct? 3) Wh must ou set a quadratic equation equal to zero when ou're solving it? 4) If a quadratic equation is unfactorable, does that mean it doesn't have a solution? If it is still possible to solve, then what methods could ou use? 5) Wh must = 0 when ou're solving for the roots of a quadratic? 6) How are the verte point and the ais of smmetr of a quadratic related to one another? 7) Is it possible to onl have one root? If so, then when is it possible? B k2m0kl6o ]KHujtKa` FSjogfGtIwda_rret BLtLMCd.b ] ZAflUlp HrEiSgBhUtQsF rrteis]eirbvsehd_.k [ emkajddep twfibtehl IpnGfTiAnSiktAeX UAZlGg[erbZrpaI Ru. --

2 8) If an equation if unfactorable, does it mean it doesn't have an roots? If not, then how can we calculate what the roots are? 9) Wh is solving a quadratic equation the same as finding it's roots? 0) What is the quadratic formula? ) What is the minimum amount of information ou need to write the equation of a parabola? 2) Describe the graph of = 5 2 compared to = ) Describe the graph of = 2 2 compared to = 2 2 Solve each equation b factoring. 4) n 2 = n 5) k 2 = 4k + 2 O X2]0eS6r ckauqtqar ksaoofvtwcagrwes VLZLUCJ.D U HAHlFlc jrqi^g\hdtksa QrbeAsjelrtvVePd^.N R UMBawdper owyigtkh[ KIsnsfdivnliAtue\ carlmgce`bcrfad CC. -2-

3 6) -3b 2-7b - 8 = -4b 2 7) = - Solve each equation b completing the square. 8) = 0 9) 2m 2 + 4m - 2 = 0 20) a 2 + 0a + 4 = -2 2) 2n 2 + 4n - 7 = 3 m f2c0\e6u KFuYtDah ASqocfVtjwUaHrJec YLfLZCW.T Y NA_llR WrUiDgahGtzsp Grjekssemr[vMeddz.D _ PMUandbeP OwwiItGhU PIInEfviineiKtbeL EAGlIgbePbarYaP M[. -3-

4 Solve each equation with the quadratic formula. 22) 4n 2-0n - 6 = 0 23) 4 p 2-5 p - 4 = 7 24) 4b 2 = 90-2b 25) = - Determine which method ou should use to solve the equation and then solve it. 26) k 2 + 4k - = -2 27) 2 p p = 7 l F2S0kp6I rkbuktuan BSsofdtrwOaorUe flwlucn.u o UAwlAlz ZrXizgIhCtvsI nrqegsterwvweid.^ ^ smvaddces WwzitqhL eiqnbfniqnriktheo AAHl`g^efbHrSaN Zj. -4-

5 Algebraicall find the Ais of Smmetr, Verte Point, & Roots. Then create a table of at least 3 coordinates to help sketch the graph of each function. 28) = ) = ) f () = ) f () = r I2g0Ga6P EKouCtjaU _SToqfmtFwapriei kldlccs.p Q kapljlz SrZi^gMhXtEsS fr`ehstelrtvfetdf._ I om[ahdvea bwiktehl NIDnmfNiHnUiutAeI iailigoevbyruac AH. -5-

6 Answer each of the following questions: 32) The height of a rocket is given b the f () = a. What is the maimum height of the rocket and after how man seconds will it reach that height? b. How man total seconds was the rocket in the air? 33) Let f () = a. if = 0, what is f()? 34) Let f () = a. if = -3, what is f()? b. if = -2 what is f()? b. if = 2 what is f()? c. If f() = 5 what is? c. If f() = 3, what are the two values of? Use the following information to write the equation of the parabola. 35) Roots: = -, Point on the Parabola: (0, -2) 36) Verte Point: (-3, -6) Point on the Parabola: (-, -2) n _2Y0O6o BKturteaZ OSrogfLtawVamrpeM QLlLfCP.J O ZAgl\lm `rgiegihytlso qrnewsceqrvvgendj.u w imha]dmeu [wti_tghb UI[nOfFikn[iRtse TAFldg[eNbrLaX N. -6-

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