Thread: [SOLVED] Convert parabola to standard form

2y^2 + x - 16y + 26 = 0

- x = 2y^2 - 16y + 26 (Moved x to the other side)

- x = 2(y^2 - 8y + 13) (Factored out 2)

x = - 2(y^2 - 8y + 13) (Divide sides by -1)

x + 26 = - 2(y^2 - 8y) (Move 13 to the left side, but first multiply it by -2, resulting in -26, therefore add 26 to each side)

x + 26 + 32 = - 2(y^2 - 8y + 16) (Complete the square on the right side, add 16 to both sides, but it has to be multiplied by -2 before I bring it to the left side, which results in -32, therefore add 32 to the left side.

x + 58 = - 2(y-4)^2

x = - 2(y-4)^2 - 58

This answer is wrong, where did I go wrong?

Originally Posted by Phire

2y^2 + x - 16y + 26 = 0

- x = 2y^2 - 16y + 26 (Moved x to the other side)

- x = 2(y^2 - 8y + 13) (Factored out 2)

x = - 2(y^2 - 8y + 13) (Divide sides by -1)

x + 26 = - 2(y^2 - 8y) (Move 13 to the left side, but first multiply it by -2, resulting in -26, therefore add 26 to each side)

x + 26 + 32 = - 2(y^2 - 8y + 16) (Complete the square on the right side, add 16 to both sides, but it has to be multiplied by -2 before I bring it to the left side, which results in -32, therefore add 32 to the left side.

x + 58 = - 2(y-4)^2

x = - 2(y-4)^2 - 58

This answer is wrong, where did I go wrong?

The red plus sign should be a minus sign. Expand the right hand side and you'll see why (you have essentially substracted 32 from the right hand side).

Originally Posted by mr fantastic

The red plus sign should be a minus sign. Expand the right hand side and you'll see why (you have essentially substracted 32 from the right hand side).

I'm still confused, if I expand:

- 2(y^2 - 8y + 16)

I get:

2y^2 + 16y - 32

Originally Posted by Phire

x + 26 + 32 =

...

2y^2 + 16y - 32

You are adding 32 to the left side, but subtracting 32 from the right. This is not a valid step.

Wow, I confused the heck out of myself, but I understand now. Thanks.