anonymous
  • anonymous
how do i start this? Find an equation for all the lines which pass through the origin and which are tangent to the parabola 푦=−푥^2+6푥−4. There may be 1, 2, or more lines.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
whoa i don't know what THAT was but it's supposed to say \[y=-x^2+6x-4\]
anonymous
  • anonymous
start by saying that if the line is tangent to the graph then the derivative is the slope, so at that the slope between \[(0,0)\] and \[(x,-x^2+6x-4)\] must be \[-2x+6\]
anonymous
  • anonymous
slope between \[(0,0)\ \text{ and } (x,-x^2+6x-4)\] is \[\frac{-x^2+6x-4-0}{x-0}=\frac{-x^2+6x-4}{x}\]

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anonymous
  • anonymous
set this equal to \[-2x+6\] and solve for x
anonymous
  • anonymous
i.e solve \[\frac{-x^2+6x-4}{x}=-2x+6\] \[-x^2+6x-4=-2x^2+6x\] etc
anonymous
  • anonymous
you have a quadratic equation, you should get two values for x
amistre64
  • amistre64
at most 2 :)
anonymous
  • anonymous
yes, at most!
anonymous
  • anonymous
an in fact exactly 2, one of which is itself exactly 2 if i am not mistaken
anonymous
  • anonymous
can you go on? i'm stuck :/ thank thus far!
anonymous
  • anonymous
\[-x^2+6x-4=-2x^2+6x\] \[x^2-4=0\] \[(x+2)(x-2)=0\] \[x=-2, x=2\]
anonymous
  • anonymous
thanks!

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