Algebra Examples

$y^{2} = x + 9$

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 $x$ .

${(0)}^{2} = x + 9$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $x + 9 = {(0)}^{2}$ .

$x + 9 = {(0)}^{2}$

Step 1.2.2

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

$x + 9 = 0$

Step 1.2.3

Subtract $9$ from both sides of the equation.

$x = - 9$

Step 1.3

x-intercept(s) in point form.

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

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 $y$ .

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

Step 2.2

Solve the equation.

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Step 2.2.1

Add $0$ and $9$ .

$y^{2} = 9$

Step 2.2.2

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

$y = \pm \sqrt{9}$

Step 2.2.3

Simplify $\pm \sqrt{9}$ .

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Step 2.2.3.1

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

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

Step 2.2.3.2

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

$y = \pm 3$

Step 2.2.4

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

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Step 2.2.4.1

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

$y = 3$

Step 2.2.4.2

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

$y = - 3$

Step 2.2.4.3

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

$y = 3, - 3$

Step 2.3

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4