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ZnappyDooZ

  • one year ago

Geometry Help Please!

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  1. Vocaloid
    • one year ago
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    hm, not quite, do you know how to complete the square?

  2. Vocaloid
    • one year ago
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    ok, just look at the x part (x^2 + 2x) if you add 1, you get x^2 + 2x + 1 which equals (x+1)^2 do you understand where the 1 comes from?

  3. Vocaloid
    • one year ago
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    I mean, do you understand why I added 1?

  4. Vocaloid
    • one year ago
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    Nope, I didn't do anything to the 2x I only added 1 so I could rewrite (x^2 + 2x) in the form (x+1)^2

  5. Vocaloid
    • one year ago
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    (x^2 + 2x + 1) = (x+1)^2

  6. Vocaloid
    • one year ago
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    (a+b)^2 = (a^2 + 2ab + b^2), have you seen this formula before?

  7. Vocaloid
    • one year ago
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    Well, it's kinda hard to explain, but you want to rewrite (x^2 + 2x) in the form (a+b)^2 or (a-b)^2 by adding a number

  8. Vocaloid
    • one year ago
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    can you try rewriting (y^2 + 4y + ___) in the form (y+b)^2? can you try filling in the blank so you get an expression in the form (y+b)^2

  9. Vocaloid
    • one year ago
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    in other words, what value should we add to make the expression equal to (y+b)^2 where b is a constant? i'm sorry, this is hard to explain D:

  10. Vocaloid
    • one year ago
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    ok, I'll give you a hint: we can add a number to y^2 + 4y to get (y+2)^2 what is that number?

  11. Vocaloid
    • one year ago
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    hint: try expanding (y+2)^2 = (y+2)(y+2)

  12. Vocaloid
    • one year ago
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    what is (y+2)(y+2)?

  13. Vocaloid
    • one year ago
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    yup! and how do we get from y^2 + 4y to y^2 + 4y + 4?

  14. Vocaloid
    • one year ago
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    this might be helpful in explaining the concept, http://www.purplemath.com/modules/sqrcircle.htm

  15. Vocaloid
    • one year ago
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    nope, you add 4 to the expression

  16. Vocaloid
    • one year ago
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    alright, I think I might have a better way to explain this...

  17. Vocaloid
    • one year ago
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    ok, after all the math we just did, we have: (x+1)^2 + (y+2)^2 = 20 + 4 + 1 remember, we added 4 and 1 to the left side, so we must add 4 and 1 to the right side

  18. Vocaloid
    • one year ago
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    (x+1)^2 + (y+2)^2 = 25, are you with me so far?

  19. Vocaloid
    • one year ago
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    alright, you know that the general equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where r is the radius and (h,k) is the center, right?

  20. Vocaloid
    • one year ago
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    can you tell me what h, k, and r are, based on what we just found out?

  21. Vocaloid
    • one year ago
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    not quite, check your math again check the signs on h and k, and check r r^2 = 25, so what is r?

  22. Vocaloid
    • one year ago
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    right, and what are h and k?

  23. Vocaloid
    • one year ago
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    not quite! -h = 1 -k = 2 so, what are h and k?

  24. Vocaloid
    • one year ago
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    yup! make sure to check the signs! so, can you now tell me what the center and radius are?

  25. Vocaloid
    • one year ago
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    yup, good job ~

  26. Vocaloid
    • one year ago
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    that's it, look at the question again: "find the center and the radius of the circle", so you're done

  27. Vocaloid
    • one year ago
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    uh, sure

  28. Vocaloid
    • one year ago
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    actually I need to go pretty soon, can I just outline my steps for you? x^2 + 2x + y^2 + 4y = 20 (x^2+2x) + (y^2 + 4y) = 20 (x^2 + 2x + 1) + (y^2 +4y + 4) = 20 + 4 + 1 = 25 (x+1)^2 + (y+2)^2 = 25 h = -1 k = -2 r = 5

  29. Vocaloid
    • one year ago
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    ok fantastic! you did perfectly, great job ~

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