Find the x and y Intercepts f(x)=x(x-3)(3x+4)

$f (x) = x (x - 3) (3 x + 4)$

Step 1

Find the x-intercepts.

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

$0 = x (x - 3) (3 x + 4)$

Solve the equation.

Rewrite the equation as $x (x - 3) (3 x + 4) = 0$ .

$x (x - 3) (3 x + 4) = 0$

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

$x = 0$

$x - 3 = 0$

$3 x + 4 = 0$

Set $x$ equal to $0$ .

$x = 0$

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

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

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

Set $3 x + 4$ equal to $0$ and solve for $x$ .

Set $3 x + 4$ equal to $0$ .

$3 x + 4 = 0$

Solve $3 x + 4 = 0$ for $x$ .

Subtract $4$ from both sides of the equation.

$3 x = - 4$

Divide each term in $3 x = - 4$ by $3$ and simplify.

Divide each term in $3 x = - 4$ by $3$ .

$\frac{3 x}{3} = \frac{- 4}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 4}{3}$

Divide $x$ by $1$ .

$x = \frac{- 4}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{4}{3}$

The final solution is all the values that make $x (x - 3) (3 x + 4) = 0$ true.

$x = 0, 3, - \frac{4}{3}$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (3, 0), (- \frac{4}{3}, 0)$

Step 2

Find the y-intercepts.

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

$y = (0) ((0) - 3) (3 (0) + 4)$

Solve the equation.

Remove parentheses.

$y = 0 (0 - 3) (3 (0) + 4)$

Remove parentheses.

$y = (0) ((0) - 3) (3 (0) + 4)$

Simplify $(0) ((0) - 3) (3 (0) + 4)$ .

Subtract $3$ from $0$ .

$y = 0 \cdot - 3 (3 (0) + 4)$

Multiply $0$ by $- 3$ .

$y = 0 (3 (0) + 4)$

Multiply $3$ by $0$ .

$y = 0 (0 + 4)$

Add $0$ and $4$ .

$y = 0 \cdot 4$

Multiply $0$ by $4$ .

$y = 0$

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(0, 0), (3, 0), (- \frac{4}{3}, 0)$

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

Step 4

Find the x and y Intercepts f(x)=x(x-3)(3x+4)

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