algebra 2 help ill give 10 points for the right answer?

Question

in each of the following problems find the p which way the parabola opens the focus the directrix the latus rectum domain and range

4y^2=x
y^2=-16x
-36y=x^2
x^2+12y=0
-80y+2x^2=0
3y^2-12x=0
3x^2-4y=0
-24y+x^2=0
-4x+9y^2=0
x=1/2y^2
y^2=3x
x-7y^2=0
y=-2x^2
8x^2+12y=0

Answer 1

4y^2=x, opens to the right
y^2=-16x to the left
-36y=x^2 down
x^2+12y=0 down
-80y+2x^2=0 up
3y^2-12x=0 right
3x^2-4y=0 up
-24y+x^2=0 up
-4x+9y^2=0 right
x=1/2y^2 right
y^2=3x right
x-7y^2=0 rigth
y=-2x^2 down
8x^2+12y=0 down .

Answer 2

I agree, that's waaaaaaaaaay too much work for 10 measly points. Besides, if we do all tihs for you, how will you learn to do it yourself? It amazes me the amount of effort some people go to, to avoid learning.
It's really not all that hard. And in the spirit of give a man a fish, he'll eat for a day, etc, I'll give you a few clues as to get these answers for yourself.
To know which way the parabola opens, just look at whether the squared term is x or y, and if the lead coefficient on the squared term is positive or negative.
If the squared term is x, it opens up or down. It opens up if the lead coefficient is postive, and it opens down if the lead coefficeint is negative.
If the squared term is y, it opens left or right. Left if the lead coefficient is negative, right if it's positive.
The domain is the set of all possible input values, the range is the set of all possible output values. Usually the inputs are x and the outputs are y, but I see you have a few examples here where x is a function of y rather than the usual other way around. Usually with a parabola, or any polynomial function, the domain is the set of all real numbers and the range is either all reals for odd degree fuctions or all reals from a certain point onward for even degreed functions (like parabolas) This in turn can come from the vertex of your parabola, which will either be a low point or a high point. I see your exercise does not explicitly ask for the vertex but you will need this to find the range. The vertex is (-b/(2a), f(-b/(2a)) A graph can help here.
For focus, directrix, and latus rectum, the explanations and formulas for these can be found at this link:
http://www.answers.com/topic/parabola
This still leaves the question of, why should you do this? You're probably thinking, I"ll never use this stuff in real life. And maybe you won't.
But think about working out in the gym. You may develop muscles that you never use in real life. But you wouldn't rig up a hydrolic lift to do your lifting for you, because that would defeat the purpose of exercise. And what is the purpose of exercise? To become strong and coordinated, that is, to develop your body and learn how to use your abilities, to be healthy and to look good. In the same way, although you may never analysise parabolas in "real life", the skills you develop in this exercise will spill over into other areas of your brain. You'll be developing your mental muscles, learning how to use them, and growing in self respect becasue you know what you can do.
Most of these parabolas appear to have vertices on the x or y axis, so finding the focus, directrix, and latus rectum shouldn't be that hard. No one wants to do it for you any more than anyone would want to help you rig up a hydrolic lift to lift weights for you in the gym. So do it yourself, and get strong.

Answer 3

This is way too much work for 2 points or even 10.

Answer 4

That's way to much work for 10 points. 6 or 7 things for each of these 14 equations, forget it.

Answer 5

WOW: your teacher gives you way too much hw- so do it yourself instead of watching tv while you let people do it for u just for a meager 10 pts