1 Warm – up #8 Solve & Graph. Write solutions in interval notation 1. 7 −3−𝑥 −2≤ − −6−4 4−𝑥 > − −2𝑥 ≥ − 6

2 Warm – up #8 Solutions 1. 7 −3−𝑥 −2≤ − −3−𝑥 ≤ − −3−𝑥 ≤ − 10 No Solution! ∅

3 Warm – up #8 Solutions 2. −6−4 4−𝑥 > − 26 −4 4−𝑥 > − 20 4−𝑥 <5 4 – x < 5 and 4 – x > − 5 -x < 1 − x > − 9 x > − 1 and x < 9 − 1 < x < 9 (–1, 9)

4 Warm – up #8 Solutions 3. −2𝑥 ≥ − 6 All Real Numbers!! − 2x ≥ − 6 or − 2x ≤ 6 x ≤ 3 or x ≥ − 3 (–∞, ∞)

5 Homework Log Tue 10/13 Lesson 2 – 4 Learning Objective:To solve quadratic equations by factoring & completing the square Hw: #209 Pg. 128 #1 – 35 odd, WS #5 – 7

6 10/13/15 Lesson 2 – 4 Factoring & Completing the Square Day 1Advanced Math/Trig

7 Learning Objective To solve quadratic equations by factoringTo solve quadratic equations by completing the square

8 Solve by Factoring 1. 3 𝑥 2 +3𝑥−60=0 3 𝑥 2 +𝑥−20 =0 3(x + 5)(x – 4) = 0 x + 5 = 0 x – 4 = 0 {–5, 4} Common factor first 2 #s that mult to –20 5 –4 1 & add to set each factor = 0

9 Solve by Factoring 2. 𝑥 2 = 9 𝑥 2 −9=0 Difference of Squares! (x – 3)(x + 3) = 0 x – 3 = 0 x + 3 = 0 {–3, 3} Square Root Prop! 𝑥 2 = 9 𝑥 2 = 9 x = ±3 Same Answer!

10 Solve by Square Root 3. (2𝑥+3) 2 = 4 2x + 3 = ±2 2x = – 3 ± 2 x = −3 ± 2 2 x = − x = −3 − 2 2 don’t forget! −1 2 , −5 2

11 Solve by Completing the Square4. 𝑥 2 −8𝑥+28 = 4 – 28 – 28 𝑥 2 −8𝑥+ = – 24 + −8 2 2 = (−4) 2 =16 (𝑥−4) 2 =−8 x – 4 = ±2𝑖 2 𝑥 2 + bx + c Divide “b” by 2 & square it 16 16 4±2𝑖 2

12 Solve by Completing the Square5. 𝑥 2 +6𝑥+13 = 0 – 13 – 13 𝑥 2 +6𝑥+ = – = (3) 2 =9 (𝑥+3) 2 =−4 x + 3 = ±2𝑖 9 9 −3±2𝑖

13 Solve by Completing the SquareDivide every term by leading coeff. 6. 2𝑥 2 −2𝑥+1 = 𝑥 2 −𝑥+ 1 2 = 0 – 1 2 – 1 2 𝑥 2 −𝑥+ = – −1 2 2 = 1 4 (𝑥− 1 2 ) 2 =− 1 4 𝑥− = ± 𝑖 2 1 2 ± 𝑖 2 or { 1±𝑖 2 } 1 4 1 4

14 Solve by Completing the Square7. 8𝑥 2 −16𝑥+104 = 8 – 104 – 104 8𝑥 2 −16𝑥 = – 𝑥 2 −2𝑥+ = –12 + −2 2 2 = (−1) 2 =1 (𝑥−1) 2 =−11 𝑥−1 = ±𝑖 11 1±𝑖 11 1 1

15 Solve by Completing the Square8. 𝑥 2 +3𝑥+12 = 0 – 12 – 12 𝑥 2 +3𝑥+ = – = 9 4 𝑥 =− 39 4 𝑥+ 3 2 = ±𝑖 − 3 2 ± 𝑖 or −3±𝑖 9 4 9 4

16 Solve by Completing the Square9. 2𝑥 2 −9𝑥= 𝑥 2 − 9 2 𝑥+ =9+ −9 2 ÷2 2 = −9 2 ∙ = −9 4 2 = (𝑥− 9 4 ) 2 = 𝑥− = ± 15 4 𝑥= 9 4 ± 15 4 𝑥= = = 6 𝑥= 9 4 – = −6 4 = −3 2 {6, −3 2 } 81 16 81 16

17 Solve by Completing the Square10. 6𝑥 2 +8𝑥=− 𝑥 𝑥+ =− ÷2 2 = 4 3 ∙ = = 4 9 (𝑥+ 2 3 ) 2 = −74 9 4 9 4 9 𝑥 = ± 𝑖 − 2 3 ± 𝑖 Or −2±𝑖

18 Ticket Out the Door Solve by completing the square.Explain your steps. 9𝑥 2 −6𝑥+25=−9

19 Homework #209 Pg. 128 #1 – 35 odd, WS #5 – 7