Michigan State University - Diagnostic Exam

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3.10

  •   The graph of the function y = 2x2 - 5 is shifted 2 units to the right and 8 units up. Which of the following describes the equation for the new graph.

    a) y = ((2x2 - 2 ) - 5) + 8 b) y = 2(x - 3)2 + 3
      
    c) y = 2(x + 3)2 + 3 d) y = 2(x - 3)2 - 13
      
    e) y = 2(x + 3)2 - 13

Solution:
The horizontal shift has the form f (x) - → f(x - 2) and the vertical shift has the form g(x)-→g (x) + 8 . It follows that
( ) 2x2 - 5 -→ 2(x - 2)2 - 5 + 8 ⇒ y = 2(x - 2)2 + 3

Diagnostic:

If you miss this question please review transformations of functions.

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July 15, 2008