Precalculus Examples

y = x^{4} - 6

$y = x^{4} - 6$

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in

0

$0$ for

y

$y$ and solve for

x

$x$ .

0 = x^{4} - 6

$0 = x^{4} - 6$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as

x^{4} - 6 = 0

$x^{4} - 6 = 0$ .

x^{4} - 6 = 0

$x^{4} - 6 = 0$

Step 1.2.2

Add

6

$6$ to both sides of the equation.

x^{4} = 6

$x^{4} = 6$

Step 1.2.3

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

x = \pm \sqrt[4]{6}

$x = \pm \sqrt[4]{6}$

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

$\pm$ to find the first solution.

x = \sqrt[4]{6}

$x = \sqrt[4]{6}$

Step 1.2.4.2

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

x = - \sqrt[4]{6}

$x = - \sqrt[4]{6}$

Step 1.2.4.3

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

x = \sqrt[4]{6}, - \sqrt[4]{6}

$x = \sqrt[4]{6}, - \sqrt[4]{6}$

x = \sqrt[4]{6}, - \sqrt[4]{6}

$x = \sqrt[4]{6}, - \sqrt[4]{6}$

x = \sqrt[4]{6}, - \sqrt[4]{6}

$x = \sqrt[4]{6}, - \sqrt[4]{6}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s):

(\sqrt[4]{6}, 0), (- \sqrt[4]{6}, 0)

$(\sqrt[4]{6}, 0), (- \sqrt[4]{6}, 0)$

x-intercept(s):

(\sqrt[4]{6}, 0), (- \sqrt[4]{6}, 0)

$(\sqrt[4]{6}, 0), (- \sqrt[4]{6}, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in

0

$0$ for

x

$x$ and solve for

y

$y$ .

y = {(0)}^{4} - 6

$y = {(0)}^{4} - 6$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

y = 0^{4} - 6

$y = 0^{4} - 6$

Step 2.2.2

Remove parentheses.

y = {(0)}^{4} - 6

$y = {(0)}^{4} - 6$

Step 2.2.3

Simplify

{(0)}^{4} - 6

${(0)}^{4} - 6$ .

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Step 2.2.3.1

Raising

0

$0$ to any positive power yields

0

$0$ .

y = 0 - 6

$y = 0 - 6$

Step 2.2.3.2

Subtract

6

$6$ from

0

$0$ .

y = - 6

$y = - 6$

y = - 6

$y = - 6$

y = - 6

$y = - 6$

Step 2.3

y-intercept(s) in point form.

y-intercept(s):

(0, - 6)

$(0, - 6)$

y-intercept(s):

(0, - 6)

$(0, - 6)$

Step 3

List the intersections.

x-intercept(s):

(\sqrt[4]{6}, 0), (- \sqrt[4]{6}, 0)

$(\sqrt[4]{6}, 0), (- \sqrt[4]{6}, 0)$

y-intercept(s):

(0, - 6)

$(0, - 6)$

Step 4

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