Find the x and y Intercepts (x-2)(x+3)

$(x - 2) (x + 3)$

Step 1

Write $(x - 2) (x + 3)$ as an equation.

$y = (x - 2) (x + 3)$

Step 2

Find the x-intercepts.

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

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

Solve the equation.

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

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

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

$x - 2 = 0$

$x + 3 = 0$

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.

$x = 2$

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

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

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

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

$x = 2, - 3$

x-intercept(s) in point form.

x-intercept(s): $(2, 0), (- 3, 0)$

Step 3

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

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

Subtract $2$ from $0$ .

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

Add $0$ and $3$ .

$y = - 2 \cdot 3$

Multiply $- 2$ by $3$ .

$y = - 6$

y-intercept(s) in point form.

y-intercept(s): $(0, - 6)$

Step 4

List the intersections.

x-intercept(s): $(2, 0), (- 3, 0)$

y-intercept(s): $(0, - 6)$

Step 5

Find the x and y Intercepts (x-2)(x+3)

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