Algebra Examples

$y = 9 - x^{2}$

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 $x$ .

$0 = 9 - x^{2}$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $9 - x^{2} = 0$ .

$9 - x^{2} = 0$

Step 1.2.2

Subtract $9$ from both sides of the equation.

$- x^{2} = - 9$

Step 1.2.3

Divide each term in $- x^{2} = - 9$ by $- 1$ and simplify.

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Step 1.2.3.1

Divide each term in $- x^{2} = - 9$ by $- 1$ .

$\frac{- x^{2}}{- 1} = \frac{- 9}{- 1}$

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.

$\frac{x^{2}}{1} = \frac{- 9}{- 1}$

Step 1.2.3.2.2

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

$x^{2} = \frac{- 9}{- 1}$

Step 1.2.3.3

Simplify the right side.

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Step 1.2.3.3.1

Divide $- 9$ by $- 1$ .

$x^{2} = 9$

Step 1.2.4

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

$x = \pm \sqrt{9}$

Step 1.2.5

Simplify $\pm \sqrt{9}$ .

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Step 1.2.5.1

Rewrite $9$ as $3^{2}$ .

$x = \pm \sqrt{3^{2}}$

Step 1.2.5.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 3$

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.

$x = 3$

Step 1.2.6.2

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

$x = - 3$

Step 1.2.6.3

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

$x = 3, - 3$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(3, 0), (- 3, 0)$

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 $y$ .

$y = 9 - {(0)}^{2}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = 9 - 0^{2}$

Step 2.2.2

Remove parentheses.

$y = 9 - {(0)}^{2}$

Step 2.2.3

Simplify $9 - {(0)}^{2}$ .

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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 $0$ .

$y = 9 - 0$

Step 2.2.3.1.2

Multiply $- 1$ by $0$ .

$y = 9 + 0$

Step 2.2.3.2

Add $9$ and $0$ .

$y = 9$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 9)$

Step 3

List the intersections.

x-intercept(s): $(3, 0), (- 3, 0)$

y-intercept(s): $(0, 9)$

Step 4