Find the x and y Intercepts f(x)=-(3x-3)(x^2+5)

$f (x) = - (3 x - 3) (x^{2} + 5)$

Step 1

Find the x-intercepts.

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

$0 = - (3 x - 3) (x^{2} + 5)$

Solve the equation.

Rewrite the equation as $- (3 x - 3) (x^{2} + 5) = 0$ .

$- (3 x - 3) (x^{2} + 5) = 0$

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

$3 x - 3 = 0$

$x^{2} + 5 = 0$

Set $3 x - 3$ equal to $0$ and solve for $x$ .

Set $3 x - 3$ equal to $0$ .

$3 x - 3 = 0$

Solve $3 x - 3 = 0$ for $x$ .

Add $3$ to both sides of the equation.

$3 x = 3$

Divide each term in $3 x = 3$ by $3$ and simplify.

Divide each term in $3 x = 3$ by $3$ .

$\frac{3 x}{3} = \frac{3}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{3}{3}$

Divide $x$ by $1$ .

$x = \frac{3}{3}$

Simplify the right side.

Divide $3$ by $3$ .

$x = 1$

Set $x^{2} + 5$ equal to $0$ and solve for $x$ .

Set $x^{2} + 5$ equal to $0$ .

$x^{2} + 5 = 0$

Solve $x^{2} + 5 = 0$ for $x$ .

Subtract $5$ from both sides of the equation.

$x^{2} = - 5$

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

$x = \pm \sqrt{- 5}$

Simplify $\pm \sqrt{- 5}$ .

Rewrite $- 5$ as $- 1 (5)$ .

$x = \pm \sqrt{- 1 (5)}$

Rewrite $\sqrt{- 1 (5)}$ as $\sqrt{- 1} \cdot \sqrt{5}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{5}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \pm i \sqrt{5}$

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.

$x = i \sqrt{5}$

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

$x = - i \sqrt{5}$

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

$x = i \sqrt{5}, - i \sqrt{5}$

The final solution is all the values that make $- (3 x - 3) (x^{2} + 5) = 0$ true.

$x = 1, i \sqrt{5}, - i \sqrt{5}$

x-intercept(s) in point form.

x-intercept(s): $(1, 0)$

Step 2

Find the y-intercepts.

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

$y = - (3 (0) - 3) ({(0)}^{2} + 5)$

Solve the equation.

Remove parentheses.

$y = - (3 (0) - 3) (0^{2} + 5)$

Remove parentheses.

$y = - (3 (0) - 3) ({(0)}^{2} + 5)$

Simplify $- (3 (0) - 3) ({(0)}^{2} + 5)$ .

Multiply $3$ by $0$ .

$y = - (0 - 3) ({(0)}^{2} + 5)$

Subtract $3$ from $0$ .

$y = - - 3 ({(0)}^{2} + 5)$

Multiply $- 1$ by $- 3$ .

$y = 3 ({(0)}^{2} + 5)$

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

$y = 3 (0 + 5)$

Add $0$ and $5$ .

$y = 3 \cdot 5$

Multiply $3$ by $5$ .

$y = 15$

y-intercept(s) in point form.

y-intercept(s): $(0, 15)$

Step 3

List the intersections.

x-intercept(s): $(1, 0)$

y-intercept(s): $(0, 15)$

Step 4

Find the x and y Intercepts f(x)=-(3x-3)(x^2+5)

Related Questions

Support LCMGCF.com by disabling your adblocker.