Find the x and y Intercepts (x-5)(x+2)=y

$(x - 5) (x + 2) = y$

Step 1

Find the x-intercepts.

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

$(x - 5) (x + 2) = 0$

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 $0$ .

$x - 5 = 0$

$x + 2 = 0$

Set $x - 5$ equal to $0$ and solve for $x$ .

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

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

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

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

The final solution is all the values that make $(x - 5) (x + 2) = 0$ true.

$x = 5, - 2$

x-intercept(s) in point form.

x-intercept(s): $(5, 0), (- 2, 0)$

Step 2

Find the y-intercepts.

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

$((0) - 5) ((0) + 2) = y$

Solve the equation.

Rewrite the equation as $y = ((0) - 5) ((0) + 2)$ .

$y = ((0) - 5) ((0) + 2)$

Simplify $((0) - 5) ((0) + 2)$ .

Subtract $5$ from $0$ .

$y = - 5 ((0) + 2)$

Add $0$ and $2$ .

$y = - 5 \cdot 2$

Multiply $- 5$ by $2$ .

$y = - 10$

y-intercept(s) in point form.

y-intercept(s): $(0, - 10)$

Step 3

List the intersections.

x-intercept(s): $(5, 0), (- 2, 0)$

y-intercept(s): $(0, - 10)$

Step 4