Finite Math Examples

$x^{2} + {(y - 3)}^{2} = 4$

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 $x$ .

$x^{2} + {((0) - 3)}^{2} = 4$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify $x^{2} + {((0) - 3)}^{2}$ .

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Step 1.2.1.1

Subtract $3$ from $0$ .

$x^{2} + {(- 3)}^{2} = 4$

Step 1.2.1.2

Raise $- 3$ to the power of $2$ .

$x^{2} + 9 = 4$

Step 1.2.2

Move all terms not containing $x$ to the right side of the equation.

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Step 1.2.2.1

Subtract $9$ from both sides of the equation.

$x^{2} = 4 - 9$

Step 1.2.2.2

Subtract $9$ from $4$ .

$x^{2} = - 5$

Step 1.2.3

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

$x = \pm \sqrt{- 5}$

Step 1.2.4

Simplify $\pm \sqrt{- 5}$ .

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Step 1.2.4.1

Rewrite $- 5$ as $- 1 (5)$ .

$x = \pm \sqrt{- 1 (5)}$

Step 1.2.4.2

Rewrite $\sqrt{- 1 (5)}$ as $\sqrt{- 1} \cdot \sqrt{5}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{5}$

Step 1.2.4.3

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \pm i \sqrt{5}$

Step 1.2.5

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

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Step 1.2.5.1

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

$x = i \sqrt{5}$

Step 1.2.5.2

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

$x = - i \sqrt{5}$

Step 1.2.5.3

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

$x = i \sqrt{5}, - i \sqrt{5}$

Step 1.3

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

x-intercept(s): $None$

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 $y$ .

${(0)}^{2} + {(y - 3)}^{2} = 4$

Step 2.2

Solve the equation.

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Step 2.2.1

Subtract ${(0)}^{2}$ from both sides of the equation.

${(y - 3)}^{2} = 4 - {(0)}^{2}$

Step 2.2.2

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

${(y - 3)}^{2} = 4 - 0$

Step 2.2.3

Multiply $- 1$ by $0$ .

${(y - 3)}^{2} = 4 + 0$

Step 2.2.4

Add $4$ and $0$ .

${(y - 3)}^{2} = 4$

Step 2.2.5

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

$y - 3 = \pm \sqrt{4}$

Step 2.2.6

Simplify $\pm \sqrt{4}$ .

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Step 2.2.6.1

Rewrite $4$ as $2^{2}$ .

$y - 3 = \pm \sqrt{2^{2}}$

Step 2.2.6.2

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

$y - 3 = \pm 2$

Step 2.2.7

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

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Step 2.2.7.1

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

$y - 3 = 2$

Step 2.2.7.2

Move all terms not containing $y$ to the right side of the equation.

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Step 2.2.7.2.1

Add $3$ to both sides of the equation.

$y = 2 + 3$

Step 2.2.7.2.2

Add $2$ and $3$ .

$y = 5$

Step 2.2.7.3

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

$y - 3 = - 2$

Step 2.2.7.4

Move all terms not containing $y$ to the right side of the equation.

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Step 2.2.7.4.1

Add $3$ to both sides of the equation.

$y = - 2 + 3$

Step 2.2.7.4.2

Add $- 2$ and $3$ .

$y = 1$

Step 2.2.7.5

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

$y = 5, 1$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 5), (0, 1)$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, 5), (0, 1)$

Step 4