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Warm Up 𝐹𝑜𝑖𝑙 (𝑥 + 3)(2𝑥 + 2) Solving Quadratic Equations by the Quadratic Formula Refresh • Remember the GENERAL FORM of a quadratic equation is 𝒚 = 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 Where a,b and c are numbers. Practice • • • • • Write in general form and identify a,b and c. 𝑥 2 − 5𝑥 = −3 We need to add 3 to both sides 𝑥 2 − 5𝑥 + 3 a= 1 b= -5 c= 3 You try • 3𝑥 2 = 4𝑥 − 5 • Answer: 3𝑥 2 − 4𝑥 + 5 • a=3 b= -4 c=5 Try again: put in general form • 𝑥+2 𝑥−2 =6 • Answer: 𝑥 2 − 10 • a=1 b=0 c= -10 What does it mean to “solve”? • When you are asked to “solve” a quadratic, it is asking you to find the roots. THE QUADRATIC FORMULA b b 4ac x 2a 2 What do we do with it? Step 1: Put in General form, and set equation = to 0. Step 2: Identify a, b, and c in your quadratic 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄. Step 3: Substitute a.b and c into the quadratic formula. Example • 𝑦 = 𝑥 2 + 4𝑥 + 3 • a=1. b=4. c=3 • 𝑥= −𝑏± 𝑏2 −4𝑎𝑐 2𝑎 • 𝑥= −4± 42 −4∙1∙3 2∙1 Example 1 continued •𝑥= −4± 4 2 •𝑥= −4+2 2 𝑎𝑛𝑑 𝑥 = • x=-1 and x=-3 −4−2 2 WHY USE THE QUADRATIC FORMULA? The quadratic formula allows you to solve ANY quadratic equation, even if you cannot factor it. Example 2 • 2 𝑥 + 2𝑥 = 63 Answer: −9 𝑎𝑛𝑑 7 Example 3: You try 2 𝑥 • Answer: 6 , -14 + 8𝑥 − 84 Example 4: you try again! 2 𝑥 − 5𝑥 = 24 • Answer: -3, 8 You try! Start with 1 and 4, then go on to the others. 1. x 2 x 63 0 2 2. x 8 x 84 0 2 3. x 5 x 24 0 2 4. x 7 x 13 0 2 5. 3 x 2 5 x 6 0 1. 9, 7 2.(6, 14) 3. 3,8 7 i 3 4. 2 5 i 47 5. 6 Homework: • 9.7 • 1: all • 3: a and b.