Finite Math Examples

$h (x) = x^{2} + 7$

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 $x$ .

$0 = x^{2} + 7$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $x^{2} + 7 = 0$ .

$x^{2} + 7 = 0$

Step 1.2.2

Subtract $7$ from both sides of the equation.

$x^{2} = - 7$

Step 1.2.3

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

$x = \pm \sqrt{- 7}$

Step 1.2.4

Simplify $\pm \sqrt{- 7}$ .

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Step 1.2.4.1

Rewrite $- 7$ as $- 1 (7)$ .

$x = \pm \sqrt{- 1 (7)}$

Step 1.2.4.2

Rewrite $\sqrt{- 1 (7)}$ as $\sqrt{- 1} \cdot \sqrt{7}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{7}$

Step 1.2.4.3

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

$x = \pm i \sqrt{7}$

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.

$x = i \sqrt{7}$

Step 1.2.5.2

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

$x = - i \sqrt{7}$

Step 1.2.5.3

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

$x = i \sqrt{7}, - i \sqrt{7}$

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 $y$ .

$y = {(0)}^{2} + 7$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = 0^{2} + 7$

Step 2.2.2

Remove parentheses.

$y = {(0)}^{2} + 7$

Step 2.2.3

Simplify ${(0)}^{2} + 7$ .

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Step 2.2.3.1

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

$y = 0 + 7$

Step 2.2.3.2

Add $0$ and $7$ .

$y = 7$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 7)$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, 7)$

Step 4