Calculus Examples

$x^{2} y - x^{2} + 4 y = 0$

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 $x$ .

$x^{2} (0) - x^{2} + 4 (0) = 0$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify $x^{2} (0) - x^{2} + 4 (0)$ .

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Step 1.2.1.1

Simplify each term.

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Step 1.2.1.1.1

Multiply $x^{2}$ by $0$ .

$0 - x^{2} + 4 (0) = 0$

Step 1.2.1.1.2

Multiply $4$ by $0$ .

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

Step 1.2.1.2

Combine the opposite terms in $0 - x^{2} + 0$ .

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Step 1.2.1.2.1

Subtract $x^{2}$ from $0$ .

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

Step 1.2.1.2.2

Add $- x^{2}$ and $0$ .

$- x^{2} = 0$

Step 1.2.2

Divide each term in $- x^{2} = 0$ by $- 1$ and simplify.

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Step 1.2.2.1

Divide each term in $- x^{2} = 0$ by $- 1$ .

$\frac{- x^{2}}{- 1} = \frac{0}{- 1}$

Step 1.2.2.2

Simplify the left side.

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Step 1.2.2.2.1

Dividing two negative values results in a positive value.

$\frac{x^{2}}{1} = \frac{0}{- 1}$

Step 1.2.2.2.2

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

$x^{2} = \frac{0}{- 1}$

Step 1.2.2.3

Simplify the right side.

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Step 1.2.2.3.1

Divide $0$ by $- 1$ .

$x^{2} = 0$

Step 1.2.3

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

$x = \pm \sqrt{0}$

Step 1.2.4

Simplify $\pm \sqrt{0}$ .

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Step 1.2.4.1

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

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

Step 1.2.4.2

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

$x = \pm 0$

Step 1.2.4.3

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 $y$ .

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

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify ${(0)}^{2} y - {(0)}^{2} + 4 y$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

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

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

Step 2.2.1.1.2

Multiply $0$ by $y$ .

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

Step 2.2.1.1.3

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

$0 - 0 + 4 y = 0$

Step 2.2.1.1.4

Multiply $- 1$ by $0$ .

$0 + 0 + 4 y = 0$

Step 2.2.1.2

Combine the opposite terms in $0 + 0 + 4 y$ .

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Step 2.2.1.2.1

Add $0$ and $0$ .

$0 + 4 y = 0$

Step 2.2.1.2.2

Add $0$ and $4 y$ .

$4 y = 0$

Step 2.2.2

Divide each term in $4 y = 0$ by $4$ and simplify.

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Step 2.2.2.1

Divide each term in $4 y = 0$ by $4$ .

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

Step 2.2.2.2

Simplify the left side.

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Step 2.2.2.2.1

Cancel the common factor of $4$ .

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Step 2.2.2.2.1.1

Cancel the common factor.

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

Step 2.2.2.2.1.2

Divide $y$ by $1$ .

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

Step 2.2.2.3

Simplify the right side.

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Step 2.2.2.3.1

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