Find the x and y Intercepts (x-4)(x-2)=y

$(x - 4) (x - 2) = y$

Step 1

Find the x-intercepts.

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

$(x - 4) (x - 2) = 0$

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 $0$ .

$x - 4 = 0$

$x - 2 = 0$

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

Set $x - 2$ equal to $0$ and solve for $x$ .

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

The final solution is all the values that make $(x - 4) (x - 2) = 0$ true.

$x = 4, 2$

x-intercept(s) in point form.

x-intercept(s): $(4, 0), (2, 0)$

Step 2

Find the y-intercepts.

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

$((0) - 4) ((0) - 2) = y$

Solve the equation.

Rewrite the equation as $y = ((0) - 4) ((0) - 2)$ .

$y = ((0) - 4) ((0) - 2)$

Simplify $((0) - 4) ((0) - 2)$ .

Subtract $4$ from $0$ .

$y = - 4 ((0) - 2)$

Subtract $2$ from $0$ .

$y = - 4 \cdot - 2$

Multiply $- 4$ by $- 2$ .

$y = 8$

y-intercept(s) in point form.

y-intercept(s): $(0, 8)$

Step 3

List the intersections.

x-intercept(s): $(4, 0), (2, 0)$

y-intercept(s): $(0, 8)$

Step 4