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## Activating Strategy

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**Activating Strategy**Sitback, watch, and be observant! Then write down something we haven’t discussed that was in the video.**Topic 2: Solving Quadratic Equations**Algebra II: Unit 2 How are quadratic equations solved by factoring, quadratic formula, taking the square root? Book: 5.2, 5.3, 5.6**Vocab**Polynomial ~ any expression with more than one term Monomial ~ an expression with one term Binomial ~ an expression with two terms Trinomial ~ an expression with three terms**Factoring**• A process used to rewrite a polynomial as a product of other polynomials having equal or lesser degree. • Ex) x2 + 8x + 15 = (x + 3)(x + 5) • Notice if you FOIL (x + 3)(x + 5) you get x2 + 8x + 15 • FOILING and FACTORING are opposites**Factoring x2 + bx + c(Reverse FOIL Method)**• x2 + 11x + 30 • x2 – 12x – 28**Your Turn…**Factor the following trinomials. If it cannot be factored answer “Not Factorable.” x2 + 5x + 4 x2 + 13x + 40 x2– 4x + 3 x2– 16x + 50**Your Turn…**Factor the following trinomials. If it cannot be factored answer “Not Factorable.” x2 + 9x + 14 x2– 8x + 12 x2– 4x + 6 x2+ 3x – 10**Solving x2 + bx + c(can’t isolate “x”)**• Zero Product Property • If A·B = 0, then A = 0 or B = 0 • Example: x2 + 3x – 18 = 0 • In topic 1, what would have been in the “0” place? • What does that tell us about the solutions we just found? • What quadratic form does solving relate to? • This is why we call it finding the zeros!!**Your Turn…**Solve the following trinomials using the zero product property. x2 + 4x + 3 = 0 x2 + 13x + 30 = 0 x2– 5x – 6 = 0 x2– 2x + 1 = 0**Factoring ax2 + bx + c(Reverse FOIL Method or Box Method)**• 3x2 - 17x + 10 • 4x2 – 4x – 3**Your Turn…**Factor the following trinomials. If it cannot be factored answer “Not Factorable.” 2x2 + 7x + 3 5x2 – 7x + 2 3x2 + 17x + 10 8x2 + 18x + 9**Solving ax2 + bx + c(can’t isolate “x”)**• Zero Product Property • If A·B = 0, then A = 0 or B = 0 • Example: 3x2 + x – 2 = 0 • In topic 1, what would have been in the “0” place? • What does that tell us about the solutions we just found? • What quadratic form does solving relate to? • This is why we call it finding the zeros!!**Your Turn…**Solve the following trinomials using the zero product property. 7x2 + 10x + 3 = 0 5x2+ 7x + 2 = 0 8x2 – 22x + 5 = 0 2x2– 5x – 25 = 0**Summarizing Strategy**When solving a quadratic equation, describe what you are specifically finding on the quadratics graph.**Practice**5.2 Practice B WS #1 – 12: just factor #13 – 24: set = 0 and solve**Activating Strategy**• Solve: x2 + 3x – 10 = 0 • Solve: 3x2 – x – 4 = 0**Topic 2: Solving Quadratic Equations**Algebra II: Unit 2 How are quadratic equations solved by factoring, quadratic formula, taking the square root? Book: 5.2, 5.3, 5.6**Factoring a2 – b2(Reverse FOIL Method or Difference of 2**Squares) • x2 – 9 • 25x2 – 36 VERY IMPORTANT ~ ONLY WORKS WITH SUBTRACTION…NOT ADDITION!**Your Turn…**Factor the following binomials. If it cannot be factored write “Not Factorable.” x2 – 16 4x2 – 49 49x2 + 4 16x2– 9**Solving a2 – b2**• Zero Product Property • If A·B = 0, then A = 0 or B = 0 • Example: 4x2 – 25 = 0 • In topic 1, what would have been in the “0” place? • What does that tell us about the solutions we just found? • What quadratic form does solving relate to? • This is why we call it finding the zeros!!**Your Turn…**Solve the following binomials using the zero product property. x2 – 9 = 0 4x2 – 81 = 0 49x2 – 16 = 0 16x2– 1 = 0**Let’s Start Over…and make things easier!**Before using any of the methods we have learned about so far we should first check for a GCF from now on! GRAPHIC ORGANIZER**Factoring with a GCF(Factor Tree)**• 5x2 – 20 • 6x2 + 15x + 9**Solving with a GCF(Factor Tree)**• 2x2 + 8x = 0 • 4x2 + 4x + 4 = 0**Factoring with a GCF(Factor Tree)**Factor/Solve/Both? 2x2 – 17x + 45 = 3x – 5**Your Turn…**Solve the following using the zero product property. 3x – 6 = x2 – 10 x2 + 19x + 88 = 0 x2 + 9x = -20**Summarizing Strategy**Explain the mistake shown below. x2+ 4x + 3 = 8 (x + 3)(x + 1) = 8 x + 3 = 8 or x + 1 = 8 x = 5 or x = 7**Practice**5.2 Practice B WS #25 – 33: just factor #34 – 45: set = 0 and solve**Activating Strategy**Solve: -4x2 + 36 = 0**Topic 2: Solving Quadratic Equations**Algebra II: Unit 2 How are quadratic equations solved by factoring, quadratic formula, taking the square root? Book: 5.2, 5.3, 5.6**Vocab**A number r is a square root of a number s if r2 = s**Simplfying Radicals**• No radicand has a perfect square factor other than one. • No radical in the denominator.**Classwork**2.2 Radicals Practice WS**Solving by Square Root**(3)(3) = 9 (-3)(-3) = 9 Very Important: If you take a square root when solving, you must use +/-**Solving by Square Root(can isolate “x”)**1/3(x + 5)2 = 7 Get (something)2 by itself first! • 2x2 + 1 = 17**Your Turn…**Solve by taking the square root. 2(x – 3)2 = 8 x = 1 and 5 -3(x +2)2 = -18 x = -2 6 ¼(x – 8)2 = 7 x = 8 27**Application**• The height, h, of an object dropped from an initial height, h0, is modeled by the equation: h = -16t2 +h0 where t is the number of seconds after the object has been dropped. • An object is dropped from the top of a 100 foot building. • How high is it after 1 second? • How long until the object hits the ground?**Summarizing Strategy**How do you know when you should solve by factoring or solve by taking the square root?**Practice**Pg. 267 #4 – 17 all**Activating Strategy**• Solve: 2x2 – 8x – 10 = 0 • Solve: 4x2 + 11 = 35**Topic 2: Solving Quadratic Equations**Algebra II: Unit 2 How are quadratic equations solved by factoring, quadratic formula, taking the square root? Book: 5.2, 5.3, 5.6**Remember**Solutions are where the graph crosses the x-axis. These are called zeros or roots.**What are the 2 methods of solving a quadratic equation that**we have learned so far? Factoring Square rooting Completing the square Quadratic Formula**Quadratic Formula**Ever hear this? A 3rd method of solving ANY quadratic equation is by using the quadratic formula. If ax2 + bx + c = 0 then…**Solving using the Quadratic Formula**Steps Get into standard form and set = 0 Fill a, b, and c into the quadratic formula 2x2 + x = 5**Solving using the Quadratic Formula**Steps Get into standard form and set = 0 Fill a, b, and c into the quadratic formula x2 - x = 5x - 9**Solving using the Quadratic Formula**Steps Get into standard form and set = 0 Fill a, b, and c into the quadratic formula 10x2 + 8x – 1 = 0**Discriminant**• The expression under the radical sign, b2 – 4ac • Can be used to determine the equation’s # of solutions and type of solutions