Precalculus Examples

${(y - 2)}^{2} = 5 (x + 2)$

Step 1

Solve for $y$ .

Tap for more steps...

Step 1.1

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

$y - 2 = \pm \sqrt{5 (x + 2)}$

Step 1.2

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

Tap for more steps...

Step 1.2.1

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

$y - 2 = \sqrt{5 (x + 2)}$

Step 1.2.2

Add $2$ to both sides of the equation.

$y = \sqrt{5 (x + 2)} + 2$

Step 1.2.3

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

$y - 2 = - \sqrt{5 (x + 2)}$

Step 1.2.4

Add $2$ to both sides of the equation.

$y = - \sqrt{5 (x + 2)} + 2$

Step 1.2.5

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

$y = \sqrt{5 (x + 2)} + 2$

$y = - \sqrt{5 (x + 2)} + 2$

$y = \sqrt{5 (x + 2)} + 2$

$y = - \sqrt{5 (x + 2)} + 2$

$y = \sqrt{5 (x + 2)} + 2$

$y = - \sqrt{5 (x + 2)} + 2$

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 $\sqrt{5 (x + 2)} + 2, - \sqrt{5 (x + 2)} + 2$ .

$y = \sqrt{5 (x + 2)} + 2$

$y = - \sqrt{5 (x + 2)} + 2$

Step 4