Find the x and y Intercepts P(x)=-2(x-3)(x-11)

$P (x) = - 2 (x - 3) (x - 11)$

Step 1

Find the x-intercepts.

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

$0 = - 2 (x - 3) (x - 11)$

Solve the equation.

Rewrite the equation as $- 2 (x - 3) (x - 11) = 0$ .

$- 2 (x - 3) (x - 11) = 0$

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

$x - 3 = 0$

$x - 11 = 0$

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 $x - 11$ equal to $0$ and solve for $x$ .

Set $x - 11$ equal to $0$ .

$x - 11 = 0$

Add $11$ to both sides of the equation.

$x = 11$

The final solution is all the values that make $- 2 (x - 3) (x - 11) = 0$ true.

$x = 3, 11$

x-intercept(s) in point form.

x-intercept(s): $(3, 0), (11, 0)$

Step 2

Find the y-intercepts.

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

$y = - 2 ((0) - 3) ((0) - 11)$

Solve the equation.

Remove parentheses.

$y = - 2 (0 - 3) ((0) - 11)$

Remove parentheses.

$y = - 2 (0 - 3) (0 - 11)$

Remove parentheses.

$y = - 2 ((0) - 3) ((0) - 11)$

Simplify $- 2 ((0) - 3) ((0) - 11)$ .

Subtract $3$ from $0$ .

$y = - 2 \cdot - 3 ((0) - 11)$

Multiply $- 2$ by $- 3$ .

$y = 6 ((0) - 11)$

Subtract $11$ from $0$ .

$y = 6 \cdot - 11$

Multiply $6$ by $- 11$ .

$y = - 66$

y-intercept(s) in point form.

y-intercept(s): $(0, - 66)$

Step 3

List the intersections.

x-intercept(s): $(3, 0), (11, 0)$

y-intercept(s): $(0, - 66)$

Step 4

Find the x and y Intercepts P(x)=-2(x-3)(x-11)

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