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anonymous

  • 5 years ago

THIS is the last quadratic equation I need help with tonight, promise

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  1. anonymous
    • 5 years ago
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    \[y ^{2}+3y-3=0\] is the equation....and so far I have \[-3 + and -\sqrt{21}\over 2\]

  2. anonymous
    • 5 years ago
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    Yep.

  3. anonymous
    • 5 years ago
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    7 times 3 is 21.. so maybe i wasn't sure if they could simplify

  4. anonymous
    • 5 years ago
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    Nope. the square root of 21 is not a nice number.

  5. anonymous
    • 5 years ago
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    ok, so what I have is correct. And they are 2 real solutions?

  6. anonymous
    • 5 years ago
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    is the thing under the square root a negative number?

  7. anonymous
    • 5 years ago
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    no, so if it was -y squared it would be non real?

  8. anonymous
    • 5 years ago
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    Yes it would be non-real if a was negative in this case.

  9. anonymous
    • 5 years ago
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    or if c was positive and a was positive it would be non-real

  10. anonymous
    • 5 years ago
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    You know what we are finding with this equation right?

  11. anonymous
    • 5 years ago
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    y?

  12. anonymous
    • 5 years ago
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    Imagine we had some equation like: f(y) = y^2 + 3y -3

  13. anonymous
    • 5 years ago
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    And we graphed it. What would it look like?

  14. anonymous
    • 5 years ago
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    Where our horizontal axis is y, and the vertical axis is f(y)

  15. anonymous
    • 5 years ago
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    http://www.wolframalpha.com/input/?i=graph+f+%3D+y^2+%2B+3y+-+3

  16. anonymous
    • 5 years ago
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    When we say the expression equals 0, we are finding where this parabola crosses the horizontal axis.

  17. anonymous
    • 5 years ago
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    What is the values for y that make this curve touch the line f(y) = 0

  18. anonymous
    • 5 years ago
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    So when we don't get a real solution it means that that curve never touches the f(y)=0 line. Like this would be the graph if it was -y^2 instead. http://www.wolframalpha.com/input/?i=graph+f+%3D+-y^2+%2B+3y+-+3 And you can see that since it's opening downward it never crosses the 0 horizontal line.

  19. anonymous
    • 5 years ago
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    And this would be the graph if a and c were both positive: http://www.wolframalpha.com/input/?i=graph+f+%3D+y^2+%2B+3y+%2B+3 Again, no real solutions because the graph doesn't cross f(y)=0.

  20. anonymous
    • 5 years ago
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    I hope that helps a bit to put into context what we're doing.

  21. anonymous
    • 5 years ago
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    Sorry i was away from this site for a bit. I will check that out, looks helpful! THanks again!

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