Algebra Examples

$x^{2} - 4$

Step 1

Write $x^{2} - 4$ as an equation.

$y = x^{2} - 4$

Step 2

Find the x-intercepts.

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

$0 = x^{2} - 4$

Solve the equation.

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Rewrite the equation as $x^{2} - 4 = 0$ .

$x^{2} - 4 = 0$

Add $4$ to both sides of the equation.

$x^{2} = 4$

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

$x = \pm \sqrt{4}$

Simplify $\pm \sqrt{4}$ .

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

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

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

$x = \pm 2$

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

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

$x = 2$

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

$x = - 2$

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

$x = 2, - 2$

x-intercept(s) in point form.

x-intercept(s): $(2, 0), (- 2, 0)$

Step 3

Find the y-intercepts.

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

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

Solve the equation.

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Remove parentheses.

$y = 0^{2} - 4$

Remove parentheses.

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

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

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

$y = 0 - 4$

Subtract $4$ from $0$ .

$y = - 4$

y-intercept(s) in point form.

y-intercept(s): $(0, - 4)$

Step 4

List the intersections.

x-intercept(s): $(2, 0), (- 2, 0)$

y-intercept(s): $(0, - 4)$

Step 5