Find the x and y Intercepts f(x)=(x+3)^2-9

$f (x) = {(x + 3)}^{2} - 9$

Step 1

Find the x-intercepts.

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

$0 = {(x + 3)}^{2} - 9$

Solve the equation.

Rewrite the equation as ${(x + 3)}^{2} - 9 = 0$ .

${(x + 3)}^{2} - 9 = 0$

Add $9$ to both sides of the equation.

${(x + 3)}^{2} = 9$

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

$x + 3 = \pm \sqrt{9}$

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

$x + 3 = \pm \sqrt{3^{2}}$

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

$x + 3 = \pm 3$

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.

$x + 3 = 3$

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

Subtract $3$ from both sides of the equation.

$x = 3 - 3$

Subtract $3$ from $3$ .

$x = 0$

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

$x + 3 = - 3$

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

Subtract $3$ from both sides of the equation.

$x = - 3 - 3$

Subtract $3$ from $- 3$ .

$x = - 6$

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

$x = 0, - 6$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (- 6, 0)$

Step 2

Find the y-intercepts.

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

$y = {((0) + 3)}^{2} - 9$

Solve the equation.

Remove parentheses.

$y = {(0 + 3)}^{2} - 9$

Remove parentheses.

$y = {((0) + 3)}^{2} - 9$

Simplify ${((0) + 3)}^{2} - 9$ .

Simplify each term.

Add $0$ and $3$ .

$y = 3^{2} - 9$

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

$y = 9 - 9$

Subtract $9$ from $9$ .

$y = 0$

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(0, 0), (- 6, 0)$

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

Step 4

Find the x and y Intercepts f(x)=(x+3)^2-9

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