Algebra Examples

$y = | x | - 1$

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = | x | - 1$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $| x | - 1 = 0$ .

$| x | - 1 = 0$

Step 1.2.2

Add $1$ to both sides of the equation.

$| x | = 1$

Step 1.2.3

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

$x = \pm 1$

Step 1.2.4

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

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Step 1.2.4.1

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

$x = 1$

Step 1.2.4.2

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

$x = - 1$

Step 1.2.4.3

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

$x = 1, - 1$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(1, 0), (- 1, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = | 0 | - 1$

Step 2.2

Simplify $| 0 | - 1$ .

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Step 2.2.1

The absolute value is the distance between a number and zero. The distance between $0$ and $0$ is $0$ .

$y = 0 - 1$

Step 2.2.2

Subtract $1$ from $0$ .

$y = - 1$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 1)$

Step 3

List the intersections.

x-intercept(s): $(1, 0), (- 1, 0)$

y-intercept(s): $(0, - 1)$

Step 4