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

$f (x) = - 2 x (x - 3)$

Step 1

Find the x-intercepts.

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

$0 = - 2 x (x - 3)$

Solve the equation.

Rewrite the equation as $- 2 x (x - 3) = 0$ .

$- 2 x (x - 3) = 0$

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

$x = 0$

$x - 3 = 0$

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.

$x = 3$

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

$x = 0, 3$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (3, 0)$

Step 2

Find the y-intercepts.

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

$y = - 2 \cdot 0 ((0) - 3)$

Solve the equation.

Remove parentheses.

$y = - 2 \cdot (0 (0 - 3))$

Remove parentheses.

$y = - 2 \cdot (0 ((0) - 3))$

Simplify $- 2 \cdot (0 ((0) - 3))$ .

Subtract $3$ from $0$ .

$y = - 2 \cdot (0 \cdot - 3)$

Multiply $- 2 (0 \cdot - 3)$ .

Multiply $0$ by $- 3$ .

$y = - 2 \cdot 0$

Multiply $- 2$ by $0$ .

$y = 0$

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(0, 0), (3, 0)$

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

Step 4

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

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