Question

What is the directrix of the parabola given by the equation y = –5x2 + 60x – 176?

Answer 1

answer choices:
x= 3 19/20
y= 4 1/20
x=4 1/20
y= 2 19/20
Im completely lost on finding the directrix

Answer 2

the last one is 3 19/20 (not 2 19/20)

Answer 3

Find the vertex, then find the focus. Finally directix.

Answer 4

http://www.sciencebuddies.org/science-fair-projects/project_ideas/CompSci_img011.gif

Answer 5

here we go again
lets go slow

Answer 6

please. I understand the focus more. But this confused me.

Answer 7

\[y = -5x^2 + 60x -176\] what is your job? to make it look like
\[4p(y-k)=(x-h)^2\]
this is going to take some algebra

Answer 8

first add \(176\) to both sides

Answer 9

I just get confused with all the variables. I know how to solve equations and stuff but the formual confuses me

Answer 10

actually i have a better idea to make it somewhat easier
but you are going to have to complete the square no matter what

Answer 11

okay thankyou!

Answer 12

ok now i see i made a bush league mistake. lets start again

Answer 13

okay

Answer 14

\[y = -5x^2 + 60x -176\]
\[y=-5(x^2-12x)-176\]
\[y=-5(x-6)^2+180-176\]
\[y=-5(x-6)^2+4\]
\[y-4=-5(x-6)^2\]
\[-\frac{1}{5}(y-4)=(x-6)^2\]

Answer 15

now it is in the form you want

Answer 16

we see from our eyeballs that the vertex is \((6,4)\) and we compute \(p\) as before by solving \(4p=-\frac{1}{5}\) so \(p=-\frac{1}{20}\)

Answer 17

okay I understand that. now how do you find the directrix though? Im not lost yet

Answer 18

parabola opens down, so the focus is \(\frac{1}{20}\) units below the vertex and directrix is \(\frac{1}{20}\) units above

Answer 19

focus is therefore \((6,4-\frac{1}{20})\) or \((6,3\tfrac{19}{20})\)

Answer 20

and directrix is \(y=4+\frac{1}{20}\) or \(y=4\tfrac{1}{20}\)

Answer 21

ohh okay! its starting to make more sense nnow! thankyou again for all your help!

Answer 22

you really need a picture to see what is going
that is a crappy one
here is a better one
http://www.wolframalpha.com/input/?i=+y+%3D+%E2%80%935x2+%2B+60x+%E2%80%93+176

Answer 23

if you take the link i sent, type "parabola" before the equation, you will get everything you want
wont help on a test or quiz though