Precalculus Examples

$y^{2} = 6 - x$

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 $x$ .

${(0)}^{2} = 6 - x$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $6 - x = {(0)}^{2}$ .

$6 - x = {(0)}^{2}$

Step 1.2.2

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

$6 - x = 0$

Step 1.2.3

Subtract $6$ from both sides of the equation.

$- x = - 6$

Step 1.2.4

Divide each term in $- x = - 6$ by $- 1$ and simplify.

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Step 1.2.4.1

Divide each term in $- x = - 6$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 6}{- 1}$

Step 1.2.4.2

Simplify the left side.

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Step 1.2.4.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 6}{- 1}$

Step 1.2.4.2.2

Divide $x$ by $1$ .

$x = \frac{- 6}{- 1}$

Step 1.2.4.3

Simplify the right side.

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Step 1.2.4.3.1

Divide $- 6$ by $- 1$ .

$x = 6$

Step 1.3

x-intercept(s) in point form.

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

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 $y$ .

$y^{2} = 6 - (0)$

Step 2.2

Solve the equation.

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Step 2.2.1

Multiply $- 1$ by $0$ .

$y^{2} = 6 + 0$

Step 2.2.2

Add $6$ and $0$ .

$y^{2} = 6$

Step 2.2.3

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

$y = \pm \sqrt{6}$

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.

$y = \sqrt{6}$

Step 2.2.4.2

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

$y = - \sqrt{6}$

Step 2.2.4.3

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

$y = \sqrt{6}, - \sqrt{6}$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, \sqrt{6}), (0, - \sqrt{6})$

Step 3

List the intersections.

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

y-intercept(s): $(0, \sqrt{6}), (0, - \sqrt{6})$

Step 4