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

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

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 $0$ .

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

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

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

$- x + 2 = 0$

Solve $- x + 2 = 0$ for $x$ .

Subtract $2$ from both sides of the equation.

$- x = - 2$

Divide each term in $- x = - 2$ by $- 1$ and simplify.

Divide each term in $- x = - 2$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 2}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 2}{- 1}$

Simplify the right side.

Divide $- 2$ by $- 1$ .

$x = 2$

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): $(- 4, 0), (2, 0)$

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

Add $0$ and $4$ .

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

Multiply $- 1$ by $0$ .

$y = 4 (0 + 2)$

Add $0$ and $2$ .

$y = 4 \cdot 2$

Multiply $4$ by $2$ .

$y = 8$

y-intercept(s) in point form.

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

List the intersections.

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

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

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

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