- anonymous

A parabola is defined by the following the following equation:
x^(2)-10x-y+23=0
What are the coordinates of its vertex?

- jamiebookeater

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- amistre64

gonna have to complete the square;

- amistre64

x^2 -10x = y -23
x^2 -10x +25 = y-23 +25

- amistre64

(x-5)^2 = (y+2)

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## More answers

- amistre64

the vertex is at (5,-2) i believe

- amistre64

teh equation tells us the vertex = (5,-2)
the distance from vertex to focus or directix = 1/4
the focus is at (5,-1' 3/4)
the parabola opens upwards

- anonymous

everyone keeps telling me to complete the squares, but i don't even know how to do that. i am horrible at math.

- amistre64

complete the square is a process used to make a square complete....add the missing parts really.

- amistre64

A complete square can move freely back and forth between to forms;
(x+3)^2 = x^2 +6x +9
^^^^^^^^
this is a complete square

- amistre64

if all we had was:
x^2 +6x. then the square is missing a part to it and it is stuck in this form...

- amistre64

How the incomplete square is made tells us alot about the missing parts

- amistre64

in short, we need to take the number that is next to the 'x'.. that 6 there in this case; and split it in half

- amistre64

6/2 = 3
the missing part that we need is then 3^2
x^2 +6x +3^2 = (x+3)^2

- myininaya

THAN square so fun!

- myininaya

well he already did it above so i was late

- amistre64

lol..your just in time ;)

- myininaya

:)

- amistre64

chizz; it takes time and practice to know it good enough to be able to see it

- myininaya

never talked about directex and focus in any of my math classes? what use are these?

- amistre64

the focus and directix are geometry terms used to define a parabola; and any conic section really. It relies upon the geometric interpretation instead of the algebraic

- myininaya

oh i see

- amistre64

a parabola is:
all poionts that are equi distant from a straight line from the focus and a perpendicular line to the directix.

- anonymous

lol amistre, nice shirt? :D

- amistre64

thnx :) i made it me self.

- anonymous

seriously? ._. nice, lol np

- amistre64

before i learned about openstudy, i taught myself many things; origami, knitting, crocheting, sister annoying...you know, the basics of life ;)

- anonymous

sister annoying? that must've been an interesting experience lol. Your wife must be so grateful to have you >_<

- amistre64

ironically no :/ but i did get to drive her to the hospital yesterday and see the kids for a bit :)

- anonymous

nah, I bet she is :) but doesn't show it :P? that's nice ^_^

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