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Algebra 1 Name___________________________________ ©R M2X0n1R7w yKVuCtjao PSPoofwtow\aRrIe] MLjLwCr.w G `AMljlW kraizgOhetqsI LrNeOsne\r^vMesdt. CW52 The Quadratic Formula Date________________ Period____ Solve each equation with the quadratic formula. 1) 3a 2 - 11a - 104 = 0 2) 4x 2 - x - 21 = 0 3) 5x 2 + 12x - 9 = 0 4) p 2 + 10 p + 6 = 0 5) x 2 + 7x - 63 = -3 6) 3m 2 - 2m - 20 = -4 Find the discriminant of each quadratic equation then state the number and type of solutions. 7) -10n 2 - 7n - 5 = 0 8) 4x 2 - 3x - 1 = 0 9) 3n 2 - 6n + 3 = 0 10) 9a 2 + 6a + 1 = 0 11) -8n 2 + 6n + 5 = 0 12) -2x 2 + 10x = 0 13) -4n 2 + 8n - 4 = 0 14) 2k 2 + 4k = 0 15) -4x 2 - 6x - 3 = 0 16) -x 2 + x - 2 = 0 Solve each equation with the quadratic formula. 17) 6n 2 + 12n - 7 = 0 Find the value of c that completes the square. 18) p 2 + 15 p + c 19) a 2 + 16a + c Solve each equation by completing the square. 20) n 2 - 14n + 10 = -3 21) v 2 - 4v + 5 = 7 Worksheet by Kuta Software LLC -1- ©y b2r0r1h7F uKcuWtfad XSXoRfNtiwhaGr]ex mLMLQCH.m w kAJlXlR WrmiGgAhxtIsI BrDeSsVeEr]v`eGdq.B X qMhaLdGeM MwAictYh] sIRn_ftiwnViwt]eV yABlVgoe]bfrVa[ G1Q. 22) a 2 + 14a + 56 = 8 Worksheet by Kuta Software LLC -2- ©K x2G0g1x7Z [K\uwtQav YSjoqfKtHwJalrhex rLwLaCY.u E xAulQlo yrVi`gshVtZsX EraewsEeFrOvZeuds.B V _Mrahd`ec nwqivtQhO gIyn]fJiQn[iiteeS gAxlXgmeYborNaM Q1s. Answers to CW52 The Quadratic Formula 1) {8, -4.333} 2) {2.42, -2.17} 3) {0.6, -3} 4) {-0.641, -9.359} 5) {5, -12} 6) {2.667, -2} 7) -151; two imaginary solutions 8) 25; two real solutions 9) 0; one real solution 10) 0; one real solution 11) 196; two real solutions 12) 100; two real solutions 13) 0; one real solution 14) 16; two real solutions 15) -12; two imaginary solutions 16) -7; two imaginary solutions 17) {0.472, -2.472} 225 18) 4 19) 64 20) {13, 1} 21) {4.449, -0.449} 22) {-6, -8} Worksheet by Kuta Software LLC -3- ©P X2k0L1x7v gKLuhtRat xSToafztRwLa[rKei ULeLiCn.C ^ GAplrlk frIikgahmtosV krWejsbeTr]vleBdm.o b YMSabdpe^ YwKivtQhH FIGnLfMiXnEidtlet SA_lHgLeBbErTal n1H.