Question

Using complete the square or -b/2a , what is the vertex of:
1/2(x^2 + 4x -2) Using complete the square or -b/2a , what is the vertex of:
1/2(x^2 + 4x -2) @Mathematics

Answer 1

I'd go with x = -b/2a to find the vertex

Answer 2

I keep getting to completely different answers though.

For completing the square I get (-1,-3) and for -b/2a I get (-1,-5/2).

Answer 3

Don't use complete the square for this. Use -b/2a then check it by graphing

Answer 4

I checked it by graphing, and the answers are closer to (-1,-3). I need someone to walk me through the steps

Answer 5

I could tell you everthing that I;ve done if that would help. Maybe you could pick out my mistakes

Answer 6

I did that using -b/2a

Answer 7

Use .5(x^2+4x-2) instead of the fraction

Answer 8

Okay. Can you tell me how you did it? When I use that form, I do get -1 to begin with, but after I replace all of the x's with -1 I get a fraction

Answer 9

my 2 cents completing the square is to much of a pain in the but to do with fractions.

Answer 10

Fractions don't bother me. It only bothers me that my check didn't match the first answer that I got

Answer 11

you can also use completing the square as follows:\[\frac{1}{2(x^2+4x-2)}=\frac{1}{2((x+2)^2-6)}\]so the verticies are found when the denominator is zero, i.e.:\[2((x+2)^2-6)=0\]\[(x+2)^2=6\]\[x=-2\pm\sqrt{6}\]

Answer 12

I mean vertical asymptotes

Answer 13

I need the vertex to start off with, otherwise the whole equation would be wrong

Answer 14

Are you suggesting that the way he set up the fraction is correct?

Answer 15

have I got the equation wrong?

Answer 16

I get the feeling that this is another fail to use parentheses when typing linear fractions

Answer 17

I'll just show my work: Let me scan it really quick

Answer 18

almost done :D

Answer 19

ah - ok @hero, reading your previous answer I see the equation could have been this instead:\[0.5(x^2+4x-2)\]is this correct @Ket-kat?

Answer 20

How're are you getting there?

Answer 21

asnaseer, might post steps

Answer 22

@asnaseer: I don't think it is

Answer 23

I hate this problem

Answer 24

sorry xD I was fine until the check didn't match up

Answer 25

-2,-3 final answer

Answer 26

ok, in which case we have:\[0.5(x^2+4x-2)=0.5((x+2)^2-6)=0.5(x+2)^2-3\]which is in standard vertex form giving vertex as (-2,-3)

Answer 27

where did you get minus 6?

Answer 28

\[x^2+4x-2=x^2+4x+4-6\]and\[x^2+4x+4=(x+2)^2\]

Answer 29

? Wouldn't you have to distribute the 1/2 first and then isolate the 3rd variable? Then you subtract 2? because you add 4 the the left side?

Answer 30

And I say 2 because you'd have to mult the -4 by the 1/2 first? xO

Answer 31

-2 = 4 - 6
so I just replace the "-2" with "4-6" so that I could complete the square with the terms left on the left-hand-side

Answer 32

I'm still lost as to how you're getting the 6.

Answer 33

ok, let me try to explain more clearly

Answer 34

kay' :)

Answer 35

I hate to say it, but using -b/2a is easier

Answer 36

xD It can be.

Answer 37

\[x^2+4x-2=x^2+4x+(-2)\]\[=x^2+4x+(4-6)\]\[=x^2+4x+4-6\]\[=(x^2+4x+4)-6\]\[=(x+2)^2-6\]is that clearer?

Answer 38

so you're answer is -2,-6 ?

Answer 39

no, what I just showed was how to factorise x^2+4x-2

Answer 40

in your question, you also had a factor of 0.5 which needs to be applied

Answer 41

My twin sis' said that you're right! She just worked it out for me. YOU'RE AMAZING :D

Answer 42

We already discussed that the vertex was (-2,-3)

Answer 43

:-) thank you, I'm glad I was able to convey the essence of the process to you - these things are not easy to grasp or teach. but well done for picking it up in the end.

Answer 44

I am actually really good at these questions, but my methods didn't work on this particular equation. Thanks for teaching me a new trick :)

Answer 45

What new trick was that?

Answer 46

how to get the right answer...

Answer 47

I think the only mistake you made was not turning 1/2 into .5

Answer 48

I don't think that was it. They pretty much ignored the 1/2 until the end?

Answer 49

All you had to do after that was simply distribute the .5 to get

.5x^2+2x-1

Then you could have used -b/2a after that

Answer 50

that's exactly what I was doing, and I still had the wrong answer

Answer 51

Are you sure? Using .5 is easier than using 1/2

Trust me

Answer 52

I'm pretty sure you were using 1/2 and NOT .5 the first time around. Trust me they're the same number but not exactly the same computational wise

Answer 53

did you look at the paper I attached? Maybe you can see the mistake I made?

Answer 54

I already told you what your mistake was. Use .5 next time

Answer 55

My teacher takes of 20 points for not using fractionss... she's chinese

Answer 56

She can't take points off for that. That's silly

Answer 57

if o.5 and 1/2 are the same thing then it shouldn't make a difference xD

Answer 58

I take it that you hate decimals

Answer 59

She's the head of the math department, I'm pretty sure she can

Answer 60

I'm a lover not a hater

Answer 61

She probably can, but it isn't right. Math is already difficult. Getting the right answer should be sufficient enough

Answer 62

@Ket-kat - you make me laugh - you have an acute sense of humour - seriously :O)
@hero and @Ket-kat - there is no right or wrong method - just one that works best for you for the problem given to you

Answer 63

Well the answer calls for 1/2 to begin with

Answer 64

1/2 = .5

Answer 65

The answer doesn't have .5 in it

Answer 66

@ Asnaseer : MAHAL KITA ;D Same to you Bre

Answer 67

or 1/2

Answer 68

My Textbook proves you otherwise, sorry xo

Answer 69

The problem has 1/2 in it, not the answer. You must be confuzzled

Answer 70

@Ket-kat I take it that means you are from the Philippines?

Answer 71

no, you have an easy time doing that for yourself. That applies to me 100 fold

Answer 72

I'm from America. I just happen to be a Pinay ;D

Answer 73

I have a friend at work who is from the Philippines which is how I recognised what you said immediately :-)

Answer 74

take car @Ket-kat

Answer 75

care**

Answer 76

Take care Asnaseer ;D It was a pleasure. Thank you for everthing

Answer 77

*ultimate fan*

Answer 78

Thanks to you too Hero :D

Answer 79

:D

Answer 80

You know I was just teasing you

Answer 81

;D

here's my nerdy face I:B (buck-teeth)