I know how to complete the square.. but im not sure what this question is asking, please help?

Question

it asks me to

complete the square and

reduce to one of the standard forms

y − b = A(x − a)^2 or x − a = A(y − b)^2

I have no idea what these standard forms have to do with completing the square....

(a) y = x^2 + 4x + 3

(b) 3x^2 + 3x + 2y = 0

so for the first and second one, what am i supposed to do?

for A do i have to make it (x+3)(x+1) = y or something...

and i have no idea what it wants me to do with this standard form thing... please help?

Answer 1

basically all you have to do is complete the square and rearrange the equation. for A, you would:

y = x^2 + 4x + 3

y = (x^2 + 4x + 4) + 3 - 4

y = (x + 2)^2 -1

Now, you want it to look like:

y − b = A(x − a)^2

So move the -1 to the other side. in this equation, A = 1, so don't worry about A.

y + 1= (x + 2)^2

and there you go! now, try to do b.

HINT: it's 3x^2 + 3x, so take out a 3 and complete the square

3x^2 + 3x + 2y = 0

3x^2 + 3x = - 2y

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

Now complete the square in the brackets. you should get:

-3/2(x + .5)^2 = y - 3/8

I hope that helps!