Question

Completing the square:

Answer 1

\[y=-2x-3\]

Answer 2

Is there anything more to this question?

Answer 3

\[y=x ^{2}-2x-3\]

Answer 4

sorry

Answer 5

Ah ok.

Sometimes it's easier to work with completing a square by first bringing the constant term to the other side.

Start with y + 3 = x^2 - 2x and we can go from there.

Answer 6

y+3?

Answer 7

We added 3 to both sides, so the left side becomes y + 3. This step is not necessary, but it makes completing the square clearer.

Answer 8

You should subtract 2/2 on the right

Answer 9

I dont udnerstand...

Answer 10

We started with this equation:

\[y = x^{2} - 2x - 3\]

Then, adding 3 to both sides (this is an optional step):

\[y + 3 = x^{2} - 2x\]

Take the coefficient of the x term, divide it by 2, then square it. That would be (2/2)^2 = 1.

So we add 1 to both sides.

\[y + 3 + 1 = x^{2} - 2x + 1\]
\[y + 4 = x^{2} - 2x + 1\]
Notice how the right side factors into a square now:

\[y + 4 = (x - 1)^{2}\]

Now we can subtract 4 from both sides to get a final solution:

\[y = (x - 1)^{2} - 4\]