Precalculus Examples

$y = - | x + 10 |$

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 $x$ .

$0 = - | x + 10 |$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $- | x + 10 | = 0$ .

$- | x + 10 | = 0$

Step 1.2.2

Divide each term in $- | x + 10 | = 0$ by $- 1$ and simplify.

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Step 1.2.2.1

Divide each term in $- | x + 10 | = 0$ by $- 1$ .

$\frac{- | x + 10 |}{- 1} = \frac{0}{- 1}$

Step 1.2.2.2

Simplify the left side.

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Step 1.2.2.2.1

Dividing two negative values results in a positive value.

$\frac{| x + 10 |}{1} = \frac{0}{- 1}$

Step 1.2.2.2.2

Divide $| x + 10 |$ by $1$ .

$| x + 10 | = \frac{0}{- 1}$

Step 1.2.2.3

Simplify the right side.

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Step 1.2.2.3.1

Divide $0$ by $- 1$ .

$| x + 10 | = 0$

Step 1.2.3

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

$x + 10 = \pm 0$

Step 1.2.4

Plus or minus $0$ is $0$ .

$x + 10 = 0$

Step 1.2.5

Subtract $10$ from both sides of the equation.

$x = - 10$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- 10, 0)$

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 $y$ .

$y = - | (0) + 10 |$

Step 2.2

Simplify $- | (0) + 10 |$ .

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Step 2.2.1

Add $0$ and $10$ .

$y = - | 10 |$

Step 2.2.2

The absolute value is the distance between a number and zero. The distance between $0$ and $10$ is $10$ .

$y = - 1 \cdot 10$

Step 2.2.3

Multiply $- 1$ by $10$ .

$y = - 10$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 10)$

Step 3

List the intersections.

x-intercept(s): $(- 10, 0)$

y-intercept(s): $(0, - 10)$

Step 4