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Solving Quadratic Inequalities

Solving Quadratic Inequalities. Objective: Write, solve, and graph a quadratic inequality in one and two variables. Example 1. Example 1. Example 3. Example 3. Example 3. Example 3. Example 4. Example 4. Application.

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Solving Quadratic Inequalities

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  1. Solving Quadratic Inequalities Objective: Write, solve, and graph a quadratic inequality in one and two variables.

  2. Example 1

  3. Example 1

  4. Example 3

  5. Example 3

  6. Example 3

  7. Example 3

  8. Example 4

  9. Example 4

  10. Application • A ball is thrown upward. Its position is defined by the equation .

  11. Application • A ball is thrown upward. Its position is defined by the equation . • First, we can find the zeros and the vertex.

  12. Application • A ball is thrown upward. Its position is defined by the equation . • How long does it take for the projectile to reach its maximum height? • What is the maximum height reached by the projectile?

  13. Application • A ball is thrown upward. Its position is defined by the equation . • How long does it take for the projectile to reach its maximum height? • What is the maximum height reached by the projectile? • x represents time and y represents position.

  14. Application • A ball is thrown upward. Its position is defined by the equation . • How long does it take for the projectile to reach its maximum height? • What is the maximum height reached by the projectile? • At t = 2.5 the ball reaches the maximum height of 100.

  15. Application • A ball is thrown upward. Its position is defined by the equation . • How long does it take for the projectile to reach its maximum height? • What is the maximum height reached by the projectile? • How long until the ball hits the ground?

  16. Application • A ball is thrown upward. Its position is defined by the equation . • How long does it take for the projectile to reach its maximum height? • What is the maximum height reached by the projectile? • How long until the ball hits the ground? • The ball hits the ground at t = 5, the x—intercept.

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