Question

Help please!

Answer 1

\[y=x ^{2} -8x+18\]

Answer 2

what are the vertex, focus, and directrix of the parabola with the equation?

Answer 3

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?

Answer 4

a=1 b=8 and c=18

Answer 5

b=-8

Answer 6

oh right

Answer 7

ok!

Answer 8

then here are the coordinates of the vertex:
\[\Large V = \left( { - \frac{b}{{2a}},\; - \frac{{{b^2} - 4ac}}{{4a}}} \right)\]

Answer 9

oh ok so \[V = ( -\frac{ -8 }{ 2 }, - \frac{ -8^{2} - 72 }{ 4 } )\]

Answer 10

yes!
after a simplification, we get:
\[\large V = \left( { - \frac{b}{{2a}},\; - \frac{{{b^2} - 4ac}}{{4a}}} \right) = \left( {4,2} \right)\]

Answer 11

alright! and now the focus?

Answer 12

here are the coordinates of the focus
\[\Large F = \left( { - \frac{b}{{2a}},\;\frac{{1 - {b^2} + 4ac}}{{4a}}} \right)\]

Answer 13

ok so \[F = ( -\frac{ -8 }{ 2 }, \frac{ 1+8^{2}+72 }{ 4 } ) \]

Answer 14

and I got (4, 34.25) but I don't think that's right XD

Answer 15

there is a little error of sign, since we have:
\[\large \begin{gathered}
F = \left( { - \frac{b}{{2a}},\;\frac{{1 - {b^2} + 4ac}}{{4a}}} \right) = \left( { - \frac{{ - 8}}{2},\;\frac{{1 - {8^2} + 4 \times 18}}{{4a}}} \right) = \hfill \\
\hfill \\
= \left( {4,\;\frac{9}{4}} \right) \hfill \\
\end{gathered} \]

Answer 16

oooh I see! ok thank you

Answer 17

and the equation of directrix:
\[\Large y = - \frac{{1 + {b^2} - 4ac}}{{4a}}\]

Answer 18

so its B right?

Answer 19

yes! that's right!

Answer 20

Awesome thank you so much

Answer 21

:)