Finite Math Examples

$y = (\frac{1}{4}) x^{2}$

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 $x$ .

$0 = (\frac{1}{4}) x^{2}$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $(\frac{1}{4}) x^{2} = 0$ .

$(\frac{1}{4}) x^{2} = 0$

Step 1.2.2

Multiply both sides of the equation by $4$ .

$4 (\frac{1}{4} x^{2}) = 4 \cdot 0$

Step 1.2.3

Simplify both sides of the equation.

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Step 1.2.3.1

Simplify the left side.

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Step 1.2.3.1.1

Simplify $4 (\frac{1}{4} x^{2})$ .

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Step 1.2.3.1.1.1

Combine $\frac{1}{4}$ and $x^{2}$ .

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

Step 1.2.3.1.1.2

Cancel the common factor of $4$ .

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Step 1.2.3.1.1.2.1

Cancel the common factor.

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

Step 1.2.3.1.1.2.2

Rewrite the expression.

$x^{2} = 4 \cdot 0$

Step 1.2.3.2

Simplify the right side.

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Step 1.2.3.2.1

Multiply $4$ by $0$ .

$x^{2} = 0$

Step 1.2.4

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

$x = \pm \sqrt{0}$

Step 1.2.5

Simplify $\pm \sqrt{0}$ .

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Step 1.2.5.1

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

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

Step 1.2.5.2

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

$x = \pm 0$

Step 1.2.5.3

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 $y$ .

$y = (\frac{1}{4}) {(0)}^{2}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = \frac{1}{4} \cdot 0^{2}$

Step 2.2.2

Remove parentheses.

$y = (\frac{1}{4}) {(0)}^{2}$

Step 2.2.3

Simplify $(\frac{1}{4}) {(0)}^{2}$ .

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Step 2.2.3.1

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

$y = \frac{1}{4} \cdot 0$

Step 2.2.3.2

Multiply $\frac{1}{4}$ by $0$ .

$y = 0$

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