Find the x and y Intercepts (x+6)^2-4

${(x + 6)}^{2} - 4$

Step 1

Write ${(x + 6)}^{2} - 4$ as an equation.

$y = {(x + 6)}^{2} - 4$

Step 2

Find the x-intercepts.

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

$0 = {(x + 6)}^{2} - 4$

Solve the equation.

Rewrite the equation as ${(x + 6)}^{2} - 4 = 0$ .

${(x + 6)}^{2} - 4 = 0$

Add $4$ to both sides of the equation.

${(x + 6)}^{2} = 4$

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

$x + 6 = \pm \sqrt{4}$

Simplify $\pm \sqrt{4}$ .

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

$x + 6 = \pm \sqrt{2^{2}}$

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

$x + 6 = \pm 2$

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

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

$x + 6 = 2$

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

Subtract $6$ from both sides of the equation.

$x = 2 - 6$

Subtract $6$ from $2$ .

$x = - 4$

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

$x + 6 = - 2$

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

Subtract $6$ from both sides of the equation.

$x = - 2 - 6$

Subtract $6$ from $- 2$ .

$x = - 8$

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

$x = - 4, - 8$

x-intercept(s) in point form.

x-intercept(s): $(- 4, 0), (- 8, 0)$

Step 3

Find the y-intercepts.

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

$y = {((0) + 6)}^{2} - 4$

Solve the equation.

Remove parentheses.

$y = {(0 + 6)}^{2} - 4$

Remove parentheses.

$y = {((0) + 6)}^{2} - 4$

Simplify ${((0) + 6)}^{2} - 4$ .

Simplify each term.

Add $0$ and $6$ .

$y = 6^{2} - 4$

Raise $6$ to the power of $2$ .

$y = 36 - 4$

Subtract $4$ from $36$ .

$y = 32$

y-intercept(s) in point form.

y-intercept(s): $(0, 32)$

Step 4

List the intersections.

x-intercept(s): $(- 4, 0), (- 8, 0)$

y-intercept(s): $(0, 32)$

Step 5

Find the x and y Intercepts (x+6)^2-4

Related Questions

Support LCMGCF.com by disabling your adblocker.