## Viktoria17 2 years ago Completing the square:

1. Viktoria17

\[y=-2x-3\]

2. LogicalApple

Is there anything more to this question?

3. Viktoria17

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

4. Viktoria17

sorry

5. LogicalApple

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.

6. Viktoria17

y+3?

7. LogicalApple

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.

8. LogicalApple

You should subtract 2/2 on the right

9. Viktoria17

I dont udnerstand...

10. LogicalApple

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