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F. Everything Quadratics

F. Everything Quadratics

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F. Everything Quadratics

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  1. F. Everything Quadratics Math 20: Foundations FM20.9 Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p)² + q , including: vertex intercepts domain and range axis of symmetry.

  2. Getting Started • String Art p.356

  3. What DO YOU Think? P.357

  4. 1. What is a Quadratic? • FM20.9 • Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p)² + q , including: • vertex • intercepts • domain and range • axis of symmetry.

  5. 1. What is a Quadratic? • Quadratic Relation – A relation that can be written in the standard form, where ; for example, • Parabola – The shape of the graph of any quadratic relation.

  6. Explore the Math p.359 • Grab your graphing Calculators!! • How does changing the coefficients and constant in a relation that is written in the form affect the graph of the relation?

  7. Summary p.359

  8. Practice • Ex. 7.1 (p.360) #1-6

  9. 2. Properties of Quadratic Graphs • FM20.9 • Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p)² + q , including: • vertex • intercepts • domain and range • axis of symmetry.

  10. Reflections p.362

  11. 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.

  12. Example 1

  13. Example 2

  14. Does this last Function have a max or min value?

  15. Example 3

  16. Summary p.368

  17. Practice • Ex. 7.2 (p.368) #1-16 #4-19

  18. 3. Graphing to Solve Quadratic Equations • FM20.9 • Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p)² + q , including: • vertex • intercepts • domain and range • axis of symmetry.

  19. 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

  20. Investigate the Math p.373

  21. Example 1

  22. Example 2

  23. Is it possible for a Quad Equation to have more than 2 roots?

  24. Example 3

  25. Summary p.379

  26. Practice • Ex. 6.3 (p.379) #1-13 #5-15

  27. 4. Quadratics in Factored Form • FM20.9 • Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p)² + q , including: • vertex • intercepts • domain and range • axis of symmetry.

  28. Investigate the Math p.382

  29. 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

  30. Example 1

  31. Example 2

  32. Example 3

  33. Example 4

  34. Summary p.390

  35. Practice • Ex. 7.4 (p.391) #1-16 #4-20