Give an equation for the following parabola (x-2)=(y-3)^2?

Question

possible answers:
(x+2)=(y-3)^2
2(x-2)=(y-3)^2
2(x+2)=(y-3)^2

Answer 1

For those to be possible answers you are missing something, but to work the equation like it is first clear the paranthesis by squaring (y-3)^2
y-3
y-3
------
y^2 - 3y
......- 3y +9
---------------
y^2-6y + 9

that gives you:
(x - 2) = y^2 - 6y + 9 clear paranthesis from (x - 2) by multiplying both sides of the equation by 1

x - 2 = y^2 - 6y + 9
now tranpose -2 to right side of the equation by using the additive inverse rule: That means change the sign and add. or simply subtracting.
Since it is a -2 you will use the additive inverse rule and add a +2 to both sides of the equation.

x -2 +2 + Y^2 -6y +9 + 2
which gives you:

x = y^2 -6y + 11 you can not factor this and come out with integers so you have to rewite the equation by first multiplying both sides by a -1:

-1(x-2) = -1(y-3)^2
-x + 2 = (-y +3)^2 then square (-y+3)

-y + 3
-y + 3
---------
y^2 -3y
......-3y +9
--------------
y^2 -6y +9 plug that back into your formula.

-x +2 = y^2 - 6y +9
now subtract 2 from both sides the of the equation.

-x +2 -2 = y^2 -6y +9 - 2
-x = y^2 - 6y +7
now multiply both sides by -1
x = -y^2 +6y -7
now factor:

x = (- y + 7)(y -1)
hope that helped. still think your left something out of question. But anyway that is basically the way you do it when factoring. I'm going to leave it up to you to graph and see if it is a parabola or not.

Answer 2

None of your possible answers appears to be correct. If we subtract 2 from both sides, we get:
x + 2 - 2 = (y - 3)² - 2 or
x = (y - 3)² - 2 which is one of the possible forms for the answer. We could also expand the square to get:
x = (y - 3)(y - 3) - 2
x = (y² - 6y + 9) - 2 which becomes
x = y² - 6y + 7 which is another possible form for the answer.

If this didn't answer your question, please reword the question and I'll try to give more help. Good luck!

Answer 3

None of the choices you give are equivalent to the parabola in question. Is there more to the question you may have missed?

Answer 4

None of the possible answers is equivalent to the original equation!