anonymous
  • anonymous
Help please!
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[y=x ^{2} -8x+18\]
anonymous
  • anonymous
what are the vertex, focus, and directrix of the parabola with the equation?
Michele_Laino
  • Michele_Laino
we have to refer to this general equation: \[\Large y = a{x^2} + bx + c\] by comparison with your parabola, what are the coefficients a, b, and c?

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anonymous
  • anonymous
a=1 b=8 and c=18
Michele_Laino
  • Michele_Laino
b=-8
anonymous
  • anonymous
oh right
Michele_Laino
  • Michele_Laino
ok!
Michele_Laino
  • Michele_Laino
then here are the coordinates of the vertex: \[\Large V = \left( { - \frac{b}{{2a}},\; - \frac{{{b^2} - 4ac}}{{4a}}} \right)\]
anonymous
  • anonymous
oh ok so \[V = ( -\frac{ -8 }{ 2 }, - \frac{ -8^{2} - 72 }{ 4 } )\]
Michele_Laino
  • Michele_Laino
yes! after a simplification, we get: \[\large V = \left( { - \frac{b}{{2a}},\; - \frac{{{b^2} - 4ac}}{{4a}}} \right) = \left( {4,2} \right)\]
anonymous
  • anonymous
alright! and now the focus?
Michele_Laino
  • Michele_Laino
here are the coordinates of the focus \[\Large F = \left( { - \frac{b}{{2a}},\;\frac{{1 - {b^2} + 4ac}}{{4a}}} \right)\]
anonymous
  • anonymous
ok so \[F = ( -\frac{ -8 }{ 2 }, \frac{ 1+8^{2}+72 }{ 4 } ) \]
anonymous
  • anonymous
and I got (4, 34.25) but I don't think that's right XD
Michele_Laino
  • Michele_Laino
there is a little error of sign, since we have: \[\large \begin{gathered} F = \left( { - \frac{b}{{2a}},\;\frac{{1 - {b^2} + 4ac}}{{4a}}} \right) = \left( { - \frac{{ - 8}}{2},\;\frac{{1 - {8^2} + 4 \times 18}}{{4a}}} \right) = \hfill \\ \hfill \\ = \left( {4,\;\frac{9}{4}} \right) \hfill \\ \end{gathered} \]
anonymous
  • anonymous
oooh I see! ok thank you
Michele_Laino
  • Michele_Laino
and the equation of directrix: \[\Large y = - \frac{{1 + {b^2} - 4ac}}{{4a}}\]
anonymous
  • anonymous
so its B right?
1 Attachment
Michele_Laino
  • Michele_Laino
yes! that's right!
anonymous
  • anonymous
Awesome thank you so much
Michele_Laino
  • Michele_Laino
:)

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