Precalculus Examples

$y = - x^{2} - 1$

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 $x$ .

$0 = - x^{2} - 1$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $- x^{2} - 1 = 0$ .

$- x^{2} - 1 = 0$

Step 1.2.2

Add $1$ to both sides of the equation.

$- x^{2} = 1$

Step 1.2.3

Divide each term in $- x^{2} = 1$ by $- 1$ and simplify.

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Step 1.2.3.1

Divide each term in $- x^{2} = 1$ by $- 1$ .

$\frac{- x^{2}}{- 1} = \frac{1}{- 1}$

Step 1.2.3.2

Simplify the left side.

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Step 1.2.3.2.1

Dividing two negative values results in a positive value.

$\frac{x^{2}}{1} = \frac{1}{- 1}$

Step 1.2.3.2.2

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{1}{- 1}$

Step 1.2.3.3

Simplify the right side.

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Step 1.2.3.3.1

Divide $1$ by $- 1$ .

$x^{2} = - 1$

Step 1.2.4

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

$x = \pm \sqrt{- 1}$

Step 1.2.5

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \pm i$

Step 1.2.6

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

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Step 1.2.6.1

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

$x = i$

Step 1.2.6.2

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

$x = - i$

Step 1.2.6.3

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

$x = i, - i$

Step 1.3

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

x-intercept(s): $None$

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 $y$ .

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

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

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

Step 2.2.2

Remove parentheses.

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

Step 2.2.3

Simplify $- {(0)}^{2} - 1$ .

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Step 2.2.3.1

Simplify each term.

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Step 2.2.3.1.1

Raising $0$ to any positive power yields $0$ .

$y = - 0 - 1$

Step 2.2.3.1.2

Multiply $- 1$ by $0$ .

$y = 0 - 1$

Step 2.2.3.2

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): $None$

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

Step 4