Find the x and y Intercepts (x+6)^2-1

${(x + 6)}^{2} - 1$

Step 1

Write ${(x + 6)}^{2} - 1$ as an equation.

$y = {(x + 6)}^{2} - 1$

Step 2

Find the x-intercepts.

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

$0 = {(x + 6)}^{2} - 1$

Solve the equation.

Rewrite the equation as ${(x + 6)}^{2} - 1 = 0$ .

${(x + 6)}^{2} - 1 = 0$

Add $1$ to both sides of the equation.

${(x + 6)}^{2} = 1$

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

$x + 6 = \pm \sqrt{1}$

Any root of $1$ is $1$ .

$x + 6 = \pm 1$

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.

$x + 6 = 1$

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

Subtract $6$ from both sides of the equation.

$x = 1 - 6$

Subtract $6$ from $1$ .

$x = - 5$

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

$x + 6 = - 1$

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

Subtract $6$ from both sides of the equation.

$x = - 1 - 6$

Subtract $6$ from $- 1$ .

$x = - 7$

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

$x = - 5, - 7$

x-intercept(s) in point form.

x-intercept(s): $(- 5, 0), (- 7, 0)$

Step 3

Find the y-intercepts.

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

$y = {((0) + 6)}^{2} - 1$

Solve the equation.

Remove parentheses.

$y = {(0 + 6)}^{2} - 1$

Remove parentheses.

$y = {((0) + 6)}^{2} - 1$

Simplify ${((0) + 6)}^{2} - 1$ .

Simplify each term.

Add $0$ and $6$ .

$y = 6^{2} - 1$

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

$y = 36 - 1$

Subtract $1$ from $36$ .

$y = 35$

y-intercept(s) in point form.

y-intercept(s): $(0, 35)$

Step 4

List the intersections.

x-intercept(s): $(- 5, 0), (- 7, 0)$

y-intercept(s): $(0, 35)$

Step 5

Find the x and y Intercepts (x+6)^2-1

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