Precalculus Examples

$y = | 3 {(x - 2)}^{2} - 3 |$

Step 1

Rewrite the equation as $| 3 {(x - 2)}^{2} - 3 | = y$ .

$| 3 {(x - 2)}^{2} - 3 | = y$

Step 2

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$3 {(x - 2)}^{2} - 3 = \pm y$

Step 3

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

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Step 3.1

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

$3 {(x - 2)}^{2} - 3 = y$

Step 3.2

Add $3$ to both sides of the equation.

$3 {(x - 2)}^{2} = y + 3$

Step 3.3

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

$3 {(x - 2)}^{2} - 3 = - y$

Step 3.4

Add $3$ to both sides of the equation.

$3 {(x - 2)}^{2} = - y + 3$

Step 3.5

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

$3 {(x - 2)}^{2} =$