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 $0$ .

$- x + 5 = 0$

Solve $- x + 5 = 0$ for $x$ .

Subtract $5$ from both sides of the equation.

$- x = - 5$

Divide each term in $- x = - 5$ by $- 1$ and simplify.

Divide each term in $- x = - 5$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 5}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 5}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 5}{- 1}$

Simplify the right side.

Divide $- 5$ by $- 1$ .

$x = 5$

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

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

$- x - 2 = 0$

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

Add $2$ to 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 $(- x + 5) (- x - 2) = 0$ 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 $(- (0) + 5) (- (0) - 2)$ .

Multiply $- 1$ by $0$ .

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

Add $0$ and $5$ .

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

Multiply $- 1$ by $0$ .

$y = 5 (0 - 2)$

Subtract $2$ from $0$ .

$y = 5 \cdot - 2$

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

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

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