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

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

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 $0$ .

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

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

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

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

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): $(3, 0), (- 1, 0)$

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

Subtract $3$ from $0$ .

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

Add $0$ and $1$ .

$y = - 3 \cdot 1$

Multiply $- 3$ by $1$ .

$y = - 3$

y-intercept(s) in point form.

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

List the intersections.

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

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