1. Quadratics Review y = x 2

2. Quadratics Review This graph opens upwards y = x 2

3. Quadratics Review y = x 2 y = -x 2 This graph opens downwards

4. Quadratics Review y = x 2

5. Quadratics Review y = x 2 y = 3x 2

6. Quadratics Review y = x 2 y = 3x 2 y = ¼ x 2

7. Quadratics Review

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

9. Setting up our equations:

10. 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: Initial height above ground level Horizontal velocity component is constant!

15. Setting up our equations: Initial height above ground level Horizontal velocity component is constant! Vertical velocity affected by gravity (9.81 m/s 2 )

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

17. Our Equations of Motion: In the horizontal direction: x = v x t

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

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

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

21. Our Equations of Motion: In the vertical direction y = ½g t 2 + v 0y t +y 0

22. Our Equations of Motion: In the vertical direction y = ½g t 2 + v 0y t +y 0 Vertical position at time t

23. Acceleration due to gravity Our Equations of Motion: In the vertical direction y = ½g t 2 + v 0y t +y 0 Vertical position at time t

24. Acceleration due to gravity Our Equations of Motion: In the vertical direction y = ½g t 2 + v 0y t +y 0 Vertical position at time t Initial vertical velocity

25. Acceleration due to gravity Our Equations of Motion: In the vertical direction y = ½g t 2 + v 0y t +y 0 Vertical position at time t Initial vertical velocity Initial height

26. Acceleration due to gravity Our Equations of Motion: In the vertical direction y = ½g t 2 + v 0y t +y 0 Vertical position at time t Initial vertical velocity Initial height Time

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 y = ½g t 2 + v 0y t +y 0 x = v x t