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anonymous

  • one year ago

HELP!!! How would you describe differences between the graphs of f(x)=2x^2 and g(x) = -2x^2? http://grabilla.com/05715-d66ebcd8-05dc-4152-83a4-8416f3f051a4.html

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  1. mathstudent55
    • one year ago
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    Do you know what the graph of y = x^2 looks like?

  2. anonymous
    • one year ago
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    Yes, a curve going positive into the y-axis

  3. mathstudent55
    • one year ago
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    Right. It is a parabola opening upwardly with vertex at (0, 0). Now think what multiplying the right side by 2 will do. y = 2x^2. It simply makes every y-coordinate twice as big as the corresponding coordinates in y = x^2, so it goes up faster and is a narrower parabola then the parabola of y = x^2. Ok so far?

  4. marihelenh
    • one year ago
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    One would open up and the other down.

  5. anonymous
    • one year ago
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    Yes, i get it

  6. mathstudent55
    • one year ago
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    |dw:1437449804090:dw|

  7. mathstudent55
    • one year ago
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    |dw:1437449855179:dw|

  8. anonymous
    • one year ago
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    And how would i explain the opposite?

  9. mathstudent55
    • one year ago
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    Now for y = -2x^2, every y-coordinate compared to the corresponding y-coordinate of y = 2x^2 is just the negative of it.

  10. mathstudent55
    • one year ago
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    |dw:1437449922369:dw|

  11. mathstudent55
    • one year ago
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    That means y = -2x^2 is a mirror image of y = 2x^2.

  12. anonymous
    • one year ago
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    So a reflection over y=x?

  13. anonymous
    • one year ago
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    y-axis*

  14. mathstudent55
    • one year ago
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    No, not y = x, and not y-axis. I'll show you in the figure below.

  15. mathstudent55
    • one year ago
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    |dw:1437450018634:dw|