Algebra Examples

$(x - 1) (x - 1) (x - 1) = y$

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 $x$ .

$(x - 1) (x - 1) (x - 1) = 0$

Step 1.2

Solve the equation.

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Step 1.2.1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 1 = 0$

Step 1.2.2

Set $x - 1$ equal to $0$ and solve for $x$ .

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Step 1.2.2.1

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Step 1.2.2.2

Add $1$ to both sides of the equation.

$x = 1$

Step 1.2.3

The final solution is all the values that make $(x - 1) (x - 1) (x - 1) = 0$ true.

$x = 1$

Step 1.3

x-intercept(s) in point form.

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

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 $y$ .

$((0) - 1) ((0) - 1) ((0) - 1) = y$

Step 2.2

Solve the equation.

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Step 2.2.1

Rewrite the equation as $y = ((0) - 1) ((0) - 1) ((0) - 1)$ .

$y = ((0) - 1) ((0) - 1) ((0) - 1)$

Step 2.2.2

Simplify $((0) - 1) ((0) - 1) ((0) - 1)$ .

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Step 2.2.2.1

Multiply $(0) - 1$ by $(0) - 1$ .

$y = {((0) - 1)}^{2} ((0) - 1)$

Step 2.2.2.2

Multiply ${((0) - 1)}^{2}$ by $(0) - 1$ by adding the exponents.

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Step 2.2.2.2.1

Multiply ${((0) - 1)}^{2}$ by $(0) - 1$ .

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Step 2.2.2.2.1.1

Raise $(0) - 1$ to the power of $1$ .

$y = {((0) - 1)}^{2} {((0) - 1)}^{1}$

Step 2.2.2.2.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = {((0) - 1)}^{2 + 1}$

Step 2.2.2.2.2

Add $2$ and $1$ .

$y = {((0) - 1)}^{3}$

Step 2.2.2.3

Subtract $1$ from $0$ .

$y = {(- 1)}^{3}$

Step 2.2.2.4

Raise $- 1$ to the power of $3$ .

$y = - 1$

Step 2.3

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4