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Curves PowerPoint Presentation

Curves

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Curves

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  1. Curves Dr Duxbury

  2. Quadratic graphs In a quadratic function, the highest power of x is 2 and it is of the form y = ax2 + bx + c. Are the following quadratic functions?

  3. Cubic graphs In a cubic function, the highest power of x is 3 and it is of the form y = ax3 + bx2 + cx + d. Are the following cubic functions?

  4. Drawing a quadratic graph Plot the following quadratic function: What do we do first?

  5. Set up a table finding points which are on the curve:

  6. Set up a table finding points which are on the curve:

  7. Set up a table finding points which are on the curve:

  8. Set up a table finding points which are on the curve:

  9. Set up a table finding points which are on the curve:

  10. Plot the points and join them up: y x

  11. Plot the points and join them up: y x

  12. Plot the points and join them up: y x

  13. Plot the points and join them up: y x

  14. Drawing a quadratic graph II Checking your graph looks right:

  15. Plot the points and join them up: y x

  16. Plot the points and join them up: y x

  17. Graphical Solution of Equations Solve Let Then find the values of x where the curve cuts the x-axis (that is where y=0).

  18. Graphical Solution of Equations If we were to solve this equation without using a graph, then we could factorise the equation: To solve it graphically:

  19. y The roots of a quadratic equation Solve x2 + 2x – 3 = 0 x = -3 x = 1

  20. The roots of an equation This tells us that the solution to the equation is

  21. Graphical Solution of Equations Solve

  22. y The roots of a quadratic equation Solve x2 + 2x – 3 = -2 So x = -2.5 and 0.5 x = 0.5 x = -2.5 y = -2

  23. Exercise: Plot the graph of y = x2 +3x – 4 for values of x between –5 and 2 Use your graph to find values of x such that x2 +3x – 4 = 0, x2 +3x – 4 = -4 and x2 +3x – 4 = x

  24. Solution y = 0

  25. Solution y = -4

  26. Solution y = x