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Math 20: Foundations FM20.9 Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p) + q, including: vertex intercepts domain and range axis of symmetry. F. Everything Quadratics Slide 2 Getting Started String Art p.356 Slide 3 Slide 4 Slide 5 Slide 6 What DO YOU Think? P.357 Slide 7 1. What is a Quadratic? FM20.9 Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p) + q, including: vertex intercepts domain and range axis of symmetry. Slide 8 1. What is a Quadratic? Slide 9 Slide 10 Summary p.359 Slide 11 Slide 12 Practice Ex. 7.1 (p.360) #1-6 Slide 13 2. Properties of Quadratic Graphs FM20.9 Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p) + q, including: vertex intercepts domain and range axis of symmetry. Slide 14 Slide 15 Reflections p.362 Slide 16 Vertex - The point at which the quadratic function reaches its maximum or minimum value. Axis of Symmetry - A line that separates a 2-D figure into two identical parts. For example, a parabola has a vertical axis of symmetry passing through its vertex. Slide 17 Example 1 Slide 18 Example 2 Slide 19 Does this last Function have a max or min value? Slide 20 Slide 21 Example 3 Slide 22 Slide 23 Summary p.368 Slide 24 Slide 25 Slide 26 Practice Ex. 7.2 (p.368) #1-16 #4-19 Slide 27 3. Graphing to Solve Quadratic Equations FM20.9 Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p) + q, including: vertex intercepts domain and range axis of symmetry. Slide 28 3. Graphing to Solve Quadratic Equations A zero is a number that when subbed in for the x variable it makes the equation equal to zero A zero is another name for an x-intercept Slide 29 Investigate the Math p.373 Slide 30 Example 1 Slide 31 Slide 32 Example 2 Slide 33 Is it possible for a Quad Equation to have more than 2 roots? Slide 34 Example 3 Slide 35 Summary p.379 Slide 36 Slide 37 Practice Ex. 6.3 (p.379) #1-13 #5-15 Slide 38 4. Quadratics in Factored Form FM20.9 Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p) + q, including: vertex intercepts domain and range axis of symmetry. Slide 39 Investigate the Math p.382 Slide 40 To find your x-intercepts for your quadratic you can factor the function then set each part equal to zero and solve for x. You can then also average your x-intercepts together to get your axis of symmetry Slide 41 Example 1 Slide 42 Example 2 Slide 43 Slide 44 Example 3 Slide 45 Slide 46 Example 4 Slide 47 Summary p.390 Slide 48 Slide 49 Slide 50 Practice Ex. 7.4 (p.391) #1-16 #4-20 Slide 51 5. Solving Quadratics by Factoring FM20.9 Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p) + q, including: vertex intercepts domain and range axis of symmetry. Slide 52 5. Solving Quadratics by Factoring Slide 53 When you rewrite your Quadratic equation in Standard form (=0) you can factor the equation to easily find your zeros (x- intercepts) Slide 54 How can you verify that your answers are correct? If I gave you the roots (x-intercepts) 2 and 6 can you give me the quadratic equation in standard form? Can all quadratic equations be solved by factoring? Slide 55 Example 1 Slide 56 Example 2 Slide 57 When your quadratic function is in factored from how can you tell how many roots there will be 2 or 1? Slide 58 Example 3 Slide 59 Example 4 Slide 60 Summary p.405 Slide 61 Practice Ex. 7.5 (p.405) #1-15 #3-18 Slide 62 6. Vertex Form FM20.9 Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p) + q, including: vertex intercepts domain and range axis of symmetry. Slide 63 6. Vertex Form Slide 64 Investigate the Math p.408 Read problem then go straight to the questions Slide 65 Example 1 Slide 66 Slide 67 Example 2 Slide 68 Example 3 Slide 69 Slide 70 Example 4 Slide 71 Summary p.416 Slide 72 Slide 73 Slide 74 Practice Ex. 7.6 (p.417) #1-14 #4-19 Slide 75 7. The Quadratic Formula FM20.9 Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p) + q, including: vertex intercepts domain and range axis of symmetry. Slide 76 7. The Quadratic Formula When we want to solve a quadratic function, find the roots, zeros or x-intercepts but we can not factor the function we use the Quadratic Formula The Quadratic Formula solve for x when we can not factor Slide 77 Slide 78 Example 1 Slide 79 Example 2 Slide 80 Example 3 Slide 81 Example 4 Slide 82 Summary p.427 Slide 83 Slide 84 Practice Ex. 7.7 (p.427) #1-11 #4-13 Slide 85 8. Solving Problems FM20.9 Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p) + q, including: vertex intercepts domain and range axis of symmetry. Slide 86 8. Solving Problems Slide 87 Example 2 Slide 88 Example 3 Slide 89 Example 4 Slide 90 Summary p.436 Slide 91 Practice Ex. 7.8 (p.436) #1-8 #2-12