anonymous
  • anonymous
THIS is the last quadratic equation I need help with tonight, promise
Mathematics
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anonymous
  • anonymous
THIS is the last quadratic equation I need help with tonight, promise
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
\[y ^{2}+3y-3=0\] is the equation....and so far I have \[-3 + and -\sqrt{21}\over 2\]
anonymous
  • anonymous
Yep.
anonymous
  • anonymous
7 times 3 is 21.. so maybe i wasn't sure if they could simplify

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anonymous
  • anonymous
Nope. the square root of 21 is not a nice number.
anonymous
  • anonymous
ok, so what I have is correct. And they are 2 real solutions?
anonymous
  • anonymous
is the thing under the square root a negative number?
anonymous
  • anonymous
no, so if it was -y squared it would be non real?
anonymous
  • anonymous
Yes it would be non-real if a was negative in this case.
anonymous
  • anonymous
or if c was positive and a was positive it would be non-real
anonymous
  • anonymous
You know what we are finding with this equation right?
anonymous
  • anonymous
y?
anonymous
  • anonymous
Imagine we had some equation like: f(y) = y^2 + 3y -3
anonymous
  • anonymous
And we graphed it. What would it look like?
anonymous
  • anonymous
Where our horizontal axis is y, and the vertical axis is f(y)
anonymous
  • anonymous
http://www.wolframalpha.com/input/?i=graph+f+%3D+y^2+%2B+3y+-+3
anonymous
  • anonymous
When we say the expression equals 0, we are finding where this parabola crosses the horizontal axis.
anonymous
  • anonymous
What is the values for y that make this curve touch the line f(y) = 0
anonymous
  • anonymous
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.
anonymous
  • anonymous
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.
anonymous
  • anonymous
I hope that helps a bit to put into context what we're doing.
anonymous
  • anonymous
Sorry i was away from this site for a bit. I will check that out, looks helpful! THanks again!

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