Find the x and y Intercepts f(x)=-(x+2)(x-1)(x-2)

$f (x) = - (x + 2) (x - 1) (x - 2)$

Step 1

Find the x-intercepts.

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

$0 = - (x + 2) (x - 1) (x - 2)$

Solve the equation.

Rewrite the equation as $- (x + 2) (x - 1) (x - 2) = 0$ .

$- (x + 2) (x - 1) (x - 2) = 0$

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

$x + 2 = 0$

$x - 1 = 0$

$x - 2 = 0$

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Set $x - 2$ equal to $0$ and solve for $x$ .

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

The final solution is all the values that make $- (x + 2) (x - 1) (x - 2) = 0$ true.

$x = - 2, 1, 2$

x-intercept(s) in point form.

x-intercept(s): $(- 2, 0), (1, 0), (2, 0)$

Step 2

Find the y-intercepts.

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

$y = - ((0) + 2) ((0) - 1) ((0) - 2)$

Solve the equation.

Remove parentheses.

$y = - (0 + 2) ((0) - 1) ((0) - 2)$

Remove parentheses.

$y = - (0 + 2) (0 - 1) ((0) - 2)$

Remove parentheses.

$y = - (0 + 2) (0 - 1) (0 - 2)$

Remove parentheses.

$y = - ((0) + 2) ((0) - 1) ((0) - 2)$

Simplify $- ((0) + 2) ((0) - 1) ((0) - 2)$ .

Add $0$ and $2$ .

$y = - 1 \cdot 2 ((0) - 1) ((0) - 2)$

Multiply $- 1$ by $2$ .

$y = - 2 ((0) - 1) ((0) - 2)$

Subtract $1$ from $0$ .

$y = - 2 \cdot - 1 ((0) - 2)$

Multiply $- 2$ by $- 1$ .

$y = 2 ((0) - 2)$

Subtract $2$ from $0$ .

$y = 2 \cdot - 2$

Multiply $2$ by $- 2$ .

$y = - 4$

y-intercept(s) in point form.

y-intercept(s): $(0, - 4)$

Step 3

List the intersections.

x-intercept(s): $(- 2, 0), (1, 0), (2, 0)$

y-intercept(s): $(0, - 4)$

Step 4

Find the x and y Intercepts f(x)=-(x+2)(x-1)(x-2)

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