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anonymous

  • one year ago

Given the functions f(x) = x2 + 6x − 1, g(x) = –x2 + 2, and h(x) = 2x2 − 4x + 3, rank them from least to greatest based on their axis of symmetry.

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  1. anonymous
    • one year ago
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    Treat them as if you were completing the square

  2. anonymous
    • one year ago
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    so\[x^2+6x-1=(x+3)^2-10\], the bracket sets them up looking like an a^2-10 (a=x+3), like any normal quadratic they start at a line of symmetry of x=0, so the translation of -10 means is irrelevant and the transformation +3 means the line of symmetry shifted to the left by 3 (i.e line of symmetry is x=-3)

  3. anonymous
    • one year ago
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    Try it for the rest then you can compare their lines of symmetry

  4. anonymous
    • one year ago
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    I see!

  5. anonymous
    • one year ago
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    so for the 2nd one, take out the the negative. -x^2+2=-(x^2-2), line of symmetry is x=2

  6. anonymous
    • one year ago
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    Yep! I understand now. Thank you so much!

  7. anonymous
    • one year ago
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    Whoops, I've run into some trouble again. When comparing the line of symmetry for h(x), which I found to be positive 1, I realized it can't be the right answer. What am I doing wrong?

  8. anonymous
    • one year ago
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    @14mdaz

  9. anonymous
    • one year ago
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    so factorising 2 out \[2x^2-4x+3=2(x^2-2x)+3=2(x-1)^2-1+3\] line of symmetry should be positive 1

  10. anonymous
    • one year ago
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    oh after the 2 should still be 2(((x-1)^2)-1) but that still wouldnt make a difference to the line of symmetry

  11. anonymous
    • one year ago
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    Exactly! However, according the practice module, that can't be right. Is there a possibility that f(x) is equivalent to positive 3 rather than negative as we had originally thought?

  12. anonymous
    • one year ago
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    its still gonna be +3 in the brackets so thats a -3 translation, did you type up f(x) wrong?

  13. anonymous
    • one year ago
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    Well, in the practice module, it gave these options for the ordering of the functions by line of symmetry (least to greatest):

  14. anonymous
    • one year ago
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    A. f, g, h

  15. anonymous
    • one year ago
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    B. h, g, f C. g, h, f D. h, f, g

  16. anonymous
    • one year ago
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    so it should be in the order (small to greatest), f(x), h(x), g(x) :/

  17. anonymous
    • one year ago
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    But our findings would suggest f, h, g, like you said, but it's not an option.

  18. anonymous
    • one year ago
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    It must be an error in the module.

  19. anonymous
    • one year ago
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    oh sorry i made a mistake with g

  20. anonymous
    • one year ago
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    you dont need to bracket it because its -x^2, its an upside down quadratic so its symmetry is still 0 not 2

  21. anonymous
    • one year ago
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    thus the order would be f, g, h?

  22. anonymous
    • one year ago
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    yes

  23. anonymous
    • one year ago
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    Thank you for clearing that up! I was driving myself crazy. It's funny that I didn't notice the error in g(x) either.

  24. anonymous
    • one year ago
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    it was my fault i thought -(x^2-2) was -(x-2)^2 XD

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