Question

make the expression a perfect square.

Answer 1

y^2+4y+

Answer 2

\[y ^{2}+4y+\]

Answer 3

need help

Answer 4

okay... so, this is just a matter of understanding how polynomials work... there is a geometric interpretation that is easy to follow, but it would be hard to communicate over open study... instead the following might be helpful.

expand the following:

\[(x + \frac{ 1 }{ 2 }a)^2\]

Answer 5

yeah i dont get it

Answer 6

okay... did you try expanding the equation I gave you?

Answer 7

\[(x + \frac{1}{2}a) (x + \frac{1}{2}a)\]
\[= x^2 + ax + (\frac{1}{2}a)^2\]

In the case of your equation, what would a be?

Answer 8

ok i see what u mean

Answer 9

yeah! so the idea of completing the square is getting your equation from the form:

y^2 + ay + ? to (y + ?)^2

Answer 10

the trick is finding the amount that you add to your first equation... this amount then determines what the value is going to be in the second equation.

As it turns out, this all depends on what the value of a is.

Answer 11

if you ignore the last term in the last equation I gave you, you get
\[x^2 + ax\]

compare it to your equation: \[y^2 + 4x\]

Answer 12

so in this case, your a = 4. Using the last equation I gave you, what is the amount you need to add to your equation given a=4?

Answer 13

2?

Answer 14

very close! you halved it correctly, but there was something else you needed to do. Take another look at the final term of the last equation I gave you.

Answer 15

do i square it ?

Answer 16

yes! lol, so your equation becomes...

y^2 + 4a + 4

Answer 17

o okay . thank you so much man

Answer 18

Yeah, np. lol. I bet you already figured out what the final form was by then working backwords... infact, if you know what you're doing, you can skip right to the final answer of \[(x+\frac{1}{2}a)^2\]
... which might have been what you did when you gave me your answer of 2... but I really suggest showing your work... teachers like to dock marks for skipping steps, lol