Question

Complete the square to rewrite the following equation. Identify the center and radius of the circle. You must show all work and calculations to receive credit.

x2 + 4x + y2 − 6y = −4

Answer 1

@AZ

Answer 2

as long as you are asking this question, you at least know something about the equation of a circle right?

Answer 3

Afraid not

Answer 4

We can separate this to
x^2 +4x + ___
y^2 - 6y + ___
The 2 __s can later be added to the other side

We need this as (_ +/- _)^2 so what to the power of two would bring us x^2 +4x + something, and what would bring us to y^2 - 6y + something

Answer 5

Hint:
x^2 + 4x + __ = (x+2)^2
y^2 -6y + ___ = (x-3)^2
So fill in the gaps, what are the values

Answer 6

Because I already gave you the other side (x+2)^2 and (x-3)^2 as hints
you can factor it out and find the blanks by just doing
(a+b)^2 = a^2 +2ab+b^2
(a-b)^2 = a^2 -2ab + b^2

Answer 7

And since I only want the last blank, from (x+2)^2 and (x-3)^2 just do 2^2 and -3^2

Answer 8

2 squared would be 4 and -3 squared would be 9

Answer 9

Yes so that means we have
x^2 + 4x+ 4 + y^2 -6x +9 and because we added the 4 and 9 to the right side, we have to add it back to hte right

(x^2 + 4x+4) + (y^2 -6x +9) = -4 + 4+9
Can you simplify the right, and factor the left?

Answer 10

3, (-2,3)

Answer 11

....
that's the answer yes, but you know that because I told you e.e

Answer 12

We have the left, and then we see the right 4-4+9, which is 9
SO, (x^2 + 4x+4) + (y^2 -6x +9) = 9

Answer 13

Since the right side is looking at radius, 9 is 3^2, which means that the radius is 3, since in
(x-h)^2 + (y-k)^2 = r^2, r is radius, (h,k) is the center

Answer 14

So the diameter is 9?

Answer 15

So, x^2 + 4x+4 is (x+2)^2 and (y^2 -6x+9) is (y-3)^2 so we have
(x+2)^2 + (y-3)^2 = 3^2

Answer 16

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Seafoam
So the diameter is 9?
\(\color{#0cbb34}{\text{End of Quote}}\)
... diameter is 2 times radius, and radius is 3 e.e

Answer 17

Oh shoot

Answer 18

Identify the center and radius of the circle.
So we have radius is 3

Answer 19

Then since we have
(x+2)^2 + (y-3)^2 this means that the coordinate is (-2,3), because you have to flip the signs

Answer 20

And you just have to remember to flip the signs here I suppose?

Answer 21

Yes, for example if it was
(x-2) and then (y+4)
The coordinate would be (2,-4)

Answer 22

Do you... kinda..g et how to do it? lol

Answer 23

@snowflake0531

Answer 24

Factoring:
Assuming you know how to do FOIL, we know that (a+b)(c+d) = ac+ad+bc+bd
Remember bd


For example, we have x^2 + 10x + 16, we want to factor this
Looking at x^2 we know that it will have to be
(x+ _ )(x+ _ )
We can then look at c, (in ax^2 + bx +c) and see it as 16
We see b is a positive number, so we don't need to worry about signs, but remember that is as 10x, which means that the two numbers that we need to multiply to get 16 (bd) has to add up to 10
So we can list it out
1,16
2,8
3,6
4,4

Only one pair, 2 and 8, can add up to 10x
So we know that is these two factors of 16


So then we have (x+2)(x+8)
You can also recheck using FOIL


`So, when you do those that have b and c both positive first look at the coefficient of x^2, usually when you practice factoring, it is 1, which makes it easier, as it is just (x+ _ )(x+ _ )
Then we look at C, know that 2 factors of it has to have a product of that, but also add up to the b value`



Then, we think, what if the b value is negative, but c value is positive

Example:
x^2 - 8x + 16
We know that two negatives make a positive, so the only thing that matters, is change the two plus' into minus, from (x+ _ )(x+ _ ) into (x- _ )(x- _)
So, by using this, the negative in front of b doesn't matter anymore
We list the factors of 16, and see which ones add up to 8
1, 16
2, 8
3, 6
4, 4

We can see that the pair is 4 and 4
So plugging those in, it's (x-4)(x-4),, you can also write it as (x-4)^2 if you want

`So, when you do these cases, change it to the form (x- _ )(x- _ )
And ignore the negative sign in front of the value b`


The other kinds:
for example, you could have
x^2 +x -12
We don't know the signs yet but can first set it out
(x +/- _ )(x +/- _ )
We see -12, but a positive value for b, (1x)
This means that with the two factors of -12, with one positive and one negative, the larger one must be positive to make b positive
So, we list them out
1,12
2,6
3,4
Not looking at the signs first, we can immediately cross out the first two pairs of factors, because no matter which is negative which is positive, it won't be x
For this time, I'll write them out, with the larger positive
-1,12 -> 11 --> 11x
-2,6 -> 4 ----> 4x
So, we know that it is 3 and 4, and with what I said earlier, 4 is positive, 3 is negative, because 4 plus -3 is x, which gets what we want
So we have x^2 + x -12 ---> (x-3)(x+4)
You can check using foil


So in general
When you do these
1. Check positive and negative for b and c (in ax^2 + bx +c )
2. Check the C value, write down the factors
3. Look at b value, and see which pair adds up to the b value

Answer 25

e.e you shoulda told me that you didn't know FOIL

FOIL = forward outside inside last
Like in (a+b)(c+d) forward is a times c, ac, outside is a times d, ad, inside is b times c, bc, and last is b times d, bd so
(a+b)(c+d) = ab+ad+bc+bd

Answer 26

@snowflake0531

Answer 27

Okay so start with
x^2 + 4x + y^2 − 6y = −4
Separate to
(x^2 + 4x) + (y^2-6y) = -4
Want to make them trinomials to factor, something squared
(x^2+4x+4) + (y^2 - 6y+9) = -4 + 4+9
Since I have to add to both sides^^^
Then we can change the trinomials, factor, and simplify the right
(x+2)^2 + (y-3)^2 = 9
So then it's
(x-h)^2 + (y-k)^2 =r^2
(x+2)^2 + (y-3)^2 = 3^2
where (h,k) is the center, r is radius
So then we have
(-2,3) is center, and 3 is radius

Answer 28

Alright so can I answer the question like this

x^2 + 4x + y^2 − 6y = −4

Then separate them into groups

(x^2 + 4x) + (y^2-6y) = -4

Making them trinomials and squaring

(x^2+4x+4) + (y^2 - 6y+9) = -4 + 4+9

Then we can change the trinomials, factor, and simplify the right

(x+2)^2 + (y-3)^2 = 9

So it converts to

(x-h)^2 + (y-k)^2 =r^2

(x+2)^2 + (y-3)^2 = 3^2

Where (h,k) is the center, r is radius

So then we have (-2,3) is center, and 3 is radius

Answer 29

Change
Making them trinomials and squaring

to
making them trinomials so we are able to factor it


also change
So it converts to

(x-h)^2 + (y-k)^2 =r^2

(x+2)^2 + (y-3)^2 = 3^2

it's not converting

We have (x-h)^2 + (y-k)^2 = r^2 as the base form, so with this part: Where (h,k) is the center, r is radius" and "(x+2)^2 + (y-3)^2 = 3^2" this part we can determine the center point and radius

Answer 30

Ok I changed those two sentences

Answer 31

Kkay, then the explanation stuff is great xd

Answer 32

Whoo thank god

Answer 33

On to the next one 😅

Answer 34

xdddd k

Answer 35

Just 4 more

Answer 36

And then another assignment..

Answer 37

Kay I'll help one what i can xd