Write in Standard Form x=(y-2)^2+36

$x = {(y - 2)}^{2} + 36$

Step 1

Solve for $y$ .

Rewrite the equation as ${(y - 2)}^{2} + 36 = x$ .

${(y - 2)}^{2} + 36 = x$

Subtract $36$ from both sides of the equation.

${(y - 2)}^{2} = x - 36$

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y - 2 = \pm \sqrt{x - 36}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$y - 2 = \sqrt{x - 36}$

Add $2$ to both sides of the equation.

$y = \sqrt{x - 36} + 2$

Next, use the negative value of the $\pm$ to find the second solution.

$y - 2 = - \sqrt{x - 36}$

Add $2$ to both sides of the equation.

$y = - \sqrt{x - 36} + 2$

The complete solution is the result of both the positive and negative portions of the solution.

$y = \sqrt{x - 36} + 2$

$y = - \sqrt{x - 36} + 2$

$y = \sqrt{x - 36} + 2$

$y = - \sqrt{x - 36} + 2$

$y = \sqrt{x - 36} + 2$

$y = - \sqrt{x - 36} + 2$

Step 2

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$y = a x^{2} + b x + c$

Step 3

The standard form is $\sqrt{x - 36} + 2, - \sqrt{x - 36} + 2$ .

$y = \sqrt{x - 36} + 2$

$y = - \sqrt{x - 36} + 2$

Step 4