## anonymous one year ago Help please!

1. anonymous

$y=x ^{2} -8x+18$

2. anonymous

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

3. 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?

4. anonymous

a=1 b=8 and c=18

5. Michele_Laino

b=-8

6. anonymous

oh right

7. Michele_Laino

ok!

8. Michele_Laino

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

9. anonymous

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

10. Michele_Laino

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

11. anonymous

alright! and now the focus?

12. Michele_Laino

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

13. anonymous

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

14. anonymous

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

15. Michele_Laino

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

16. anonymous

oooh I see! ok thank you

17. Michele_Laino

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

18. anonymous

so its B right?

19. Michele_Laino

yes! that's right!

20. anonymous

Awesome thank you so much

21. Michele_Laino

:)