Precalculus Examples

$y^{2} + x - 36 = 0$

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 $x$ .

${(0)}^{2} + x - 36 = 0$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify ${(0)}^{2} + x - 36$ .

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Step 1.2.1.1

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

$0 + x - 36 = 0$

Step 1.2.1.2

Add $0$ and $x$ .

$x - 36 = 0$

Step 1.2.2

Add $36$ to both sides of the equation.

$x = 36$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(36, 0)$

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 $y$ .

$y^{2} + 0 - 36 = 0$

Step 2.2

Solve the equation.

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Step 2.2.1

Add $y^{2}$ and $0$ .

$y^{2} - 36 = 0$

Step 2.2.2

Add $36$ to both sides of the equation.

$y^{2} = 36$

Step 2.2.3

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

$y = \pm \sqrt{36}$

Step 2.2.4

Simplify $\pm \sqrt{36}$ .

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Step 2.2.4.1

Rewrite $36$ as $6^{2}$ .

$y = \pm \sqrt{6^{2}}$

Step 2.2.4.2

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

$y = \pm 6$

Step 2.2.5

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

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Step 2.2.5.1

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

$y = 6$

Step 2.2.5.2

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

$y = - 6$

Step 2.2.5.3

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

$y = 6, - 6$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 6), (0, - 6)$

Step 3

List the intersections.

x-intercept(s): $(36, 0)$

y-intercept(s): $(0, 6), (0, - 6)$

Step 4