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

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

Step 1

Find the x-intercepts.

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

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

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 $0$ .

$x - 1 = 0$

$x - 3 = 0$

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 $x - 3$ 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 $(x - 1) (x - 3) = 0$ true.

$x = 1, 3$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

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

Solve the equation.

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

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

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

Subtract $1$ from $0$ .

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

Subtract $3$ from $0$ .

$y = - 1 \cdot - 3$

Multiply $- 1$ by $- 3$ .

$y = 3$

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4