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

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

Find the x-intercepts.

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

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

Solve the equation.

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

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

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x + 6 = 0$

$x^{2} - 6 = 0$

Set $x + 6$ equal to $0$ and solve for $x$ .

Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

Set $x^{2} - 6$ equal to $0$ and solve for $x$ .

Set $x^{2} - 6$ equal to $0$ .

$x^{2} - 6 = 0$

Solve $x^{2} - 6 = 0$ for $x$ .

Add $6$ to both sides of the equation.

$x^{2} = 6$

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

$x = \pm \sqrt{6}$

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.

$x = \sqrt{6}$

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

$x = - \sqrt{6}$

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

$x = \sqrt{6}, - \sqrt{6}$

The final solution is all the values that make $(x + 6) (x + 6) (x^{2} - 6) = 0$ true.

$x = - 6, \sqrt{6}, - \sqrt{6}$

x-intercept(s) in point form.

x-intercept(s): $(- 6, 0), (\sqrt{6}, 0), (- \sqrt{6}, 0)$

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

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

Add $0$ and $6$ .

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

Add $0$ and $6$ .

$y = 6 \cdot 6 ({(0)}^{2} - 6)$

Multiply $6$ by $6$ .

$y = 36 ({(0)}^{2} - 6)$

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

$y = 36 (0 - 6)$

Subtract $6$ from $0$ .

$y = 36 \cdot - 6$

Multiply $36$ by $- 6$ .

$y = - 216$

y-intercept(s) in point form.

y-intercept(s): $(0, - 216)$

List the intersections.

x-intercept(s): $(- 6, 0), (\sqrt{6}, 0), (- \sqrt{6}, 0)$

y-intercept(s): $(0, - 216)$

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

Related Questions

Support LCMGCF.com by disabling your adblocker.