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Chapter 8

Chapter 8. 8-1 Introduction to Quadratic Equations. Quadratic Equation. Any equation of degree 2. Definition. An equation of the form ax 2 + bx + c = 0, where a, b, and c are constants and a 0 is called the standard form of a quadratic equation. Examples:.

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Chapter 8

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  1. Chapter 8 8-1 Introduction to Quadratic Equations

  2. Quadratic Equation Any equation of degree 2 Definition An equation of the form ax2 + bx + c = 0, where a, b, and c are constants and a 0 is called the standard form of a quadratic equation Examples:

  3. Objective 1: Solve equations of the type ax2 + bx + c = 0 by factoring

  4. Objective 1: Solve equations of the type ax2 + bx + c = 0 by factoring

  5. Objective 1: Solve equations of the type ax2 + bx + c = 0 by factoring

  6. Objective 2: Solve quadratic equations of the form Ax2 = C by using square roots

  7. Objective 2: Solve quadratic equations of the form Ax2 = C by using square roots

  8. Objective 2: Solve quadratic equations of the form Ax2 = C by using square roots

  9. Objective 2: Solve quadratic equations of the form Ax2 = C by using square roots

  10. Objective 2: Solve quadratic equations of the form Ax2 = C by using square roots

  11. Completing the Square: A process by which you force a trinomial to be a perfect square trinomial so you can solve it using square roots.

  12. Objective 3: Solve quadratic equations by completing the square

  13. Objective 3: Solve quadratic equations by completing the square

  14. Objective 3: Solve quadratic equations by completing the square

  15. Objective 3: Solve quadratic equations by completing the square

  16. HW #8.1Pg 345-346 3-54 every third problem, 57-62

  17. Chapter 8 8-2 Using Quadratic Equations

  18. Two cyclists A and B leave the same point one traveling north and the other traveling west. B travels 7 km/h faster than A. After 3 hours they are 39 km apart. Find the speed of each cyclist.

  19. Two cyclists A and B leave the same point one traveling north and the other traveling west. B travels 7 km/h faster than A. After 3 hours they are 39 km apart. Find the speed of each cyclist.

  20. Scott wants to swim across a river that is 400 meters wide. He begins swimming perpendicular to the shore he started from but ends up 100 meters down river from where he started because of the current. How far did he actually swim from his starting point?

  21. In construction, floor space must be given for staircases. If the second floor is 3.6 meters above the first floor and a contractor is using the standard step pattern of 28 cm of tread for 18 cm of rise then how many steps are needed to get from the first to the second floor and how much linear distance will need to be used for the staircase?

  22. Chapter 8 8-3 Quadratic Formula

  23. Three objects are launched from the top of a 100-foot building. The first object is launched upward with an initial velocity of 10 feet per second. The second object is dropped. The third object is launched downward with an initial velocity of 10 feet per second.

  24. HW #8.2-3Pg 349 8-13Pg 352-353 3-36 every third, 37-52

  25. Chapter 8 8-4 Solutions of quadratic Equations

  26. Complex conjugate solutions

  27. Determine the nature of the solutions

  28. Theorem 8-4: For the equation ax2 + bx + c = 0, the sum of the solutions is , and the product of the solutions is . Find the sum and the product of the solutions of the following quadratic equations:

  29. Theorem 8-4: For the equation ax2 + bx + c = 0, the sum of the solutions is , and the product of the solutions is . Find a quadratic equation for which the sum and product of the solutions is given:

  30. Use the sum and product properties to write a quadratic equation whose solutions are given.

  31. Use the sum and product properties to write a quadratic equation whose solutions are given.

  32. Use the sum and product properties to write a quadratic equation whose solutions are given.

  33. HW #8.4Pg 357 Left Column, 56-65, 67-72

  34. Chapter 8 8.5 Equations Reducible to Quadratic Form

  35. An equation is said to be in quadratic form if it is reducible to a quadratic equation through a substitution Let u = x2

  36. HW #8.5Pg 361 1-19 Odd, 20-26

  37. Chapter 8 8.6 Formulas and Problem Solving

  38. Solve for the indicated variable:

  39. Three objects are launched from the top of a 100-foot building. The first object is launched upward with an initial velocity of 10 feet per second. The second object is dropped. The third object is launched downward with an initial velocity of 10 feet per second. How long will it take each object to hit the ground?

  40. A ladder 10 ft. long leans against a wall. The bottom of the ladder is 6 feet from the wall. How much would the lower end of the ladder have to be pulled away so that the top end be pulled down by 3 feet?

  41. HW #8.6Pg 364-365 1-29 Odd, 30

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