Find the x and y Intercepts (-x+3)(-x-1)=y

$(- x + 3) (- x - 1) = y$

Step 1

Find the x-intercepts.

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

$(- x + 3) (- x - 1) = 0$

Solve the equation.

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

$- x + 3 = 0$

$- x - 1 = 0$

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

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

$- x + 3 = 0$

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

Subtract $3$ from both sides of the equation.

$- x = - 3$

Divide each term in $- x = - 3$ by $- 1$ and simplify.

Divide each term in $- x = - 3$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 3}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 3}{- 1}$

Simplify the right side.

Divide $- 3$ by $- 1$ .

$x = 3$

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

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

$- x - 1 = 0$

Solve $- x - 1 = 0$ for $x$ .

Add $1$ to both sides of the equation.

$- x = 1$

Divide each term in $- x = 1$ by $- 1$ and simplify.

Divide each term in $- x = 1$ by $- 1$ .

$\frac{- x}{- 1} = \frac{1}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{1}{- 1}$

Divide $x$ by $1$ .

$x = \frac{1}{- 1}$

Simplify the right side.

Divide $1$ by $- 1$ .

$x = - 1$

The final solution is all the values that make $(- x + 3) (- x - 1) = 0$ true.

$x = 3, - 1$

x-intercept(s) in point form.

x-intercept(s): $(3, 0), (- 1, 0)$

Step 2

Find the y-intercepts.

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

$(- (0) + 3) (- (0) - 1) = y$

Solve the equation.

Rewrite the equation as $y = (- (0) + 3) (- (0) - 1)$ .

$y = (- (0) + 3) (- (0) - 1)$

Simplify $(- (0) + 3) (- (0) - 1)$ .

Multiply $- 1$ by $0$ .

$y = (0 + 3) (- (0) - 1)$

Add $0$ and $3$ .

$y = 3 (- (0) - 1)$

Multiply $- 1$ by $0$ .

$y = 3 (0 - 1)$

Subtract $1$ from $0$ .

$y = 3 \cdot - 1$

Multiply $3$ by $- 1$ .

$y = - 3$

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(3, 0), (- 1, 0)$

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

Step 4

Find the x and y Intercepts (-x+3)(-x-1)=y

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