Algebra Examples

$F (x) = \frac{2 x^{2}}{x^{2} + 4}$

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 $x$ .

$0 = \frac{2 x^{2}}{x^{2} + 4}$

Step 1.2

Solve the equation.

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Step 1.2.1

Set the numerator equal to zero.

$2 x^{2} = 0$

Step 1.2.2

Solve the equation for $x$ .

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Step 1.2.2.1

Divide each term in $2 x^{2} = 0$ by $2$ and simplify.

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Step 1.2.2.1.1

Divide each term in $2 x^{2} = 0$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{0}{2}$

Step 1.2.2.1.2

Simplify the left side.

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Step 1.2.2.1.2.1

Cancel the common factor of $2$ .

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Step 1.2.2.1.2.1.1

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{0}{2}$

Step 1.2.2.1.2.1.2

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

$x^{2} = \frac{0}{2}$

Step 1.2.2.1.3

Simplify the right side.

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Step 1.2.2.1.3.1

Divide $0$ by $2$ .

$x^{2} = 0$

Step 1.2.2.2

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

$x = \pm \sqrt{0}$

Step 1.2.2.3

Simplify $\pm \sqrt{0}$ .

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Step 1.2.2.3.1

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Step 1.2.2.3.2

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

$x = \pm 0$

Step 1.2.2.3.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 1.3

x-intercept(s) in point form.

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

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 $y$ .

$y = \frac{2 {(0)}^{2}}{{(0)}^{2} + 4}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = \frac{2 \cdot 0^{2}}{{(0)}^{2} + 4}$

Step 2.2.2

Remove parentheses.

$y = \frac{2 \cdot 0^{2}}{0^{2} + 4}$

Step 2.2.3

Remove parentheses.

$y = \frac{2 {(0)}^{2}}{{(0)}^{2} + 4}$

Step 2.2.4

Simplify $\frac{2 {(0)}^{2}}{{(0)}^{2} + 4}$ .

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Step 2.2.4.1

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

$y = \frac{2 \cdot 0}{0^{2} + 4}$

Step 2.2.4.2

Simplify the denominator.

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Step 2.2.4.2.1

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

$y = \frac{2 \cdot 0}{0 + 4}$

Step 2.2.4.2.2

Add $0$ and $4$ .

$y = \frac{2 \cdot 0}{4}$

Step 2.2.4.3

Simplify the expression.

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Step 2.2.4.3.1

Multiply $2$ by $0$ .

$y = \frac{0}{4}$

Step 2.2.4.3.2

Divide $0$ by $4$ .

$y = 0$

Step 2.3

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4