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Quadratic Curves

Quadratic Curves. A quadratic curve can be expressed in this form:. General Form. General Form. y. x. −1. 0. y. x. 0. 1. General Form. Look at the x-intercept to determine whether shift left or right!. y. x. How to find x-intercepts and y-intercept?. 1 and 4 are the values of the

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Quadratic Curves

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  1. Quadratic Curves

  2. A quadratic curve can be expressed in this form:

  3. General Form

  4. General Form

  5. y x −1 0 y x 0 1 General Form

  6. Look at the x-intercept to determine whether shift left or right!

  7. y x How to find x-intercepts and y-intercept? 1 and 4 are the values of the x-intercepts. In other words, the x-intercepts have coordinates (1, 0) and (4, 0) y-intercept = 4 (value of c) Line of Symmetry: x = 2.5

  8. Maximum Turning Point Minimum Turning Point Turning points

  9. y x −1 4 Find the coordinate of the turning point y-coordinate: (?, ?) x-coordinate: Turning Point is (1.5, −6.25) Does the value of a affect the turning point of the curve? No. a only affects 2 things – shape and width

  10. y x 0 1 −2 −1 2 Find the equation of the following curves:

  11. y Remember that c represents the y-intercept: x 0 −2 −1 Dotted Curve: Notice that the y-intercept of the Blue Curve is 0. How would you change the equation so that the y-intercept is 0?

  12. y x 0 1 2 Dotted Curve: Again, the y-intercept is 0

  13. One more example…find this equation y x −2 0 −7

  14. Movie http://www.youtube.com/watch?v=U2ayuow3U0c&feature=related

  15. McDonald Sign

  16. y 4 x −2 0 How many Curves do you need? 4 What is the equation of this curve?

  17. Find the equations of ALL 4 curves and draw your McDonald Sign To help you, here are the WINDOW settings:

  18. Solution:

  19. How to turn off the axes

  20. Shading 2nd PRGM (Draw)  7: SHADE  (bottom y equation, top y equation) E.g: (y3, y1), ENTER y1 y3 VARS  Y-VARS

  21. Enter Text 2nd PRGM (Draw)  0: TEXT  (ALPHA followed by letter)

  22. Storing Pic • 2nd PRGM (Draw)  STO  1: StorePic • key in a number from 1 to 9  Press enter Recalling Pic • 2nd PRGM (Draw)  STO  1: RecallPic • key in the number where you stored it  Press enter

  23. Ideas for ACE

  24. Check a 4 Steps to Quadratic Curve Sketching Solve for x Check c

  25. y 12 -3 -2 x Example: c = 12

  26. y 12 4 -3 x Example: a = -1

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