Section 8.6-8.7 Day 3 Solving 𝑎 𝑥 2 +𝑏𝑥+𝑐=0 Algebra 1

Learning Targets Factor trinomials in the form 𝑎 𝑥 2 +𝑏𝑥+𝑐 Solve algebraic equations of the form 𝑎 𝑥 2 +𝑏𝑥+𝑐=0

Multiple Variables Example 1 Factor 𝑥 2 −14𝑥𝑦−51 𝑦 2 𝑎∙𝑐=−51 𝑦 2 𝑏=−14𝑦 Answer: (𝑥+3𝑦)(𝑥−17𝑦)

Multiple Variables Example 2 Factor 𝑎 2 +10𝑎𝑏−39 𝑏 2 𝑎∙𝑐=−39 𝑏 2 𝑏=10𝑏 Answer: (𝑎+13𝑏)(𝑎−3𝑏)

2 Step Factoring – Level 1 Example 3 GCF: 4 4( 𝑎 2 +8𝑎−48) Answer: 4(𝑎−4)(𝑎+12)

2 Step Factoring: Level 1 Example 4 GCF: 2 2(−4 𝑥 2 +19𝑥+30) Answer: 2(4𝑥+5)(−𝑥+6)

2 step Factoring: Level 2 Example 6 GCF: 4𝑥 4𝑥(3 𝑥 2 −17𝑥+20) Answer: 4𝑥(3𝑥−5)(𝑥−4)

Solving 𝑎 𝑥 2 +𝑏𝑥+𝑐=0 Example 5 Solve 6 𝑥 3 −51 𝑥 2 +90𝑥=0 3𝑥 2 𝑥 2 −17𝑥+30 =0 3𝑥 𝑥−6 2𝑥−5 =0 Answer: 𝑥=0, 𝑥=6, 𝑥= 5 2

Solving 𝑎 𝑥 2 +𝑏𝑥+𝑐=0 Example 7 Solve 3 𝑛 5 −6 𝑛 4 =105 𝑛 3 Rewrite: 3 𝑛 5 −6 𝑛 4 −105 𝑛 3 =0 GCF: 3 𝑛 3 3 𝑛 3 𝑛 2 −2𝑛−35 =0 3 𝑛 3 𝑛−7 𝑛+5 =0 Answer: 𝑛=0, 𝑛=7, 𝑛=−5

Solving 𝑎 𝑥 2 +𝑏𝑥+𝑐=0 Example 8 (PG 512: #4) A person throws a ball upward from a 506-foot tall building. The ball’s height ℎ in feet after 𝑡 seconds is given by the equation ℎ= −16 𝑡 2 +48𝑡+506. The ball lands on a balcony that is 218 feet above the ground. How many seconds was it in the air? 218=−16 t 2 +48t+506 0=−16 𝑡 2 +48𝑡+288 0=−16 𝑡 2 −3𝑡+18 =−16(𝑡−6)(𝑡+3) 𝑡=6 𝑠𝑒𝑐𝑜𝑛𝑑𝑠

Problem 1 Factor 𝑥 2 +9𝑥+20 Answer: (𝑥+5)(𝑥+4)

Problem 2 Solve 2 𝑥 2 +22𝑥=−20 Answer: 2 𝑥+10 (𝑥+1) 𝑥=−10 and 𝑥=−1

Problem 3 Solve 2 𝑥 2 −3𝑥=20 Answer: 𝑥=4, 𝑥=− 5 2