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Quadratics Review

This review explores the concepts of graphing and manipulating linear and quadratic functions, with a specific focus on projectile motion. The equations of motion for both the horizontal and vertical directions are discussed, along with the effects of gravity and initial conditions.

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Quadratics Review

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  1. Quadratics Review y = x2

  2. Quadratics Review This graph opens upwards y = x2

  3. Quadratics Review y = x2 This graph opens downwards y = -x2

  4. Quadratics Review y = x2

  5. Quadratics Review y = x2 y = 3x2

  6. Quadratics Review y = ¼ x2 y = x2 y = 3x2

  7. Quadratics Review

  8. Projectile Motion Graphing and manipulating linear and quadratic functions.

  9. Setting up our equations:

  10. Setting up our equations: • In general, we take our initial x-position as x = 0

  11. Setting up our equations: • In general, we take our initial x-position as x = 0 • And we take GROUND LEVEL as y = 0

  12. Setting up our equations: • In general, we take our initial x-position as x = 0 • And we take GROUND LEVEL as y = 0 • This means that our initial y-position is often not zero!

  13. Setting up our equations: Initial height above ground level

  14. Setting up our equations: Horizontal velocity component is constant! Initial height above ground level

  15. Setting up our equations: Horizontal velocity component is constant! Vertical velocity affected by gravity (9.81 m/s2) Initial height above ground level

  16. Our Equations of Motion: • In the horizontal direction:

  17. Our Equations of Motion: • In the horizontal direction: x = vxt

  18. Our Equations of Motion: • In the horizontal direction: x = vxt Horizontal distance traveled

  19. Our Equations of Motion: • In the horizontal direction: x = vxt Horizontal distance traveled Horizontal velocity

  20. Our Equations of Motion: • In the horizontal direction: x = vxt Time Horizontal distance traveled Horizontal velocity

  21. Our Equations of Motion: • In the vertical direction y = ½gt2 + v0yt +y0

  22. Our Equations of Motion: • In the vertical direction y = ½g t2 + v0yt +y0 Vertical position at time t

  23. Our Equations of Motion: • In the vertical direction y = ½g t2 + v0yt +y0 Vertical position at time t Acceleration due to gravity

  24. Our Equations of Motion: • In the vertical direction y = ½g t2 + v0yt +y0 Vertical position at time t Initial vertical velocity Acceleration due to gravity

  25. Our Equations of Motion: • In the vertical direction y = ½g t2 + v0yt +y0 Initial height Vertical position at time t Initial vertical velocity Acceleration due to gravity

  26. Our Equations of Motion: Time • In the vertical direction y = ½g t2 + v0yt +y0 Initial height Vertical position at time t Initial vertical velocity Acceleration due to gravity

  27. Our Equations of Motion: • In the horizontal direction • In the vertical direction • Because both x and y are defined in terms of another parameter, t, we call these PARAMETRIC EQUATIONS x = vxt y = ½g t2 + v0yt +y0

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