Find the x and y Intercepts (x^2-4x-12)/(x+2)

$\frac{x^{2} - 4 x - 12}{x + 2}$

Step 1

Write $\frac{x^{2} - 4 x - 12}{x + 2}$ as an equation.

$y = \frac{x^{2} - 4 x - 12}{x + 2}$

Step 2

Find the x-intercepts.

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

$0 = \frac{x^{2} - 4 x - 12}{x + 2}$

Solve the equation.

Set the numerator equal to zero.

$x^{2} - 4 x - 12 = 0$

Solve the equation for $x$ .

Factor $x^{2} - 4 x - 12$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 12$ and whose sum is $- 4$ .

$- 6, 2$

Write the factored form using these integers.

$(x - 6) (x + 2) = 0$

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

$x - 6 = 0$

$x + 2 = 0$

Set $x - 6$ equal to $0$ and solve for $x$ .

Set $x - 6$ equal to $0$ .

$x - 6 = 0$

Add $6$ to both sides of the equation.

$x = 6$

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 $(x - 6) (x + 2) = 0$ true.

$x = 6, - 2$

Exclude the solutions that do not make $0 = \frac{x^{2} - 4 x - 12}{x + 2}$ true.

$x = 6$

x-intercept(s) in point form.

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

Step 3

Find the y-intercepts.

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

$y = \frac{{(0)}^{2} - 4 \cdot 0 - 12}{(0) + 2}$

Solve the equation.

Remove parentheses.

$y = \frac{0^{2} - 4 \cdot 0 - 12}{(0) + 2}$

Remove parentheses.

$y = \frac{0^{2} - 4 \cdot 0 - 12}{0 + 2}$

Remove parentheses.

$y = \frac{{(0)}^{2} - 4 \cdot 0 - 12}{(0) + 2}$

Simplify $\frac{{(0)}^{2} - 4 \cdot 0 - 12}{(0) + 2}$ .

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$y = \frac{0 - 4 \cdot 0 - 12}{0 + 2}$

Multiply $- 4$ by $0$ .

$y = \frac{0 + 0 - 12}{0 + 2}$

Add $0$ and $0$ .

$y = \frac{0 - 12}{0 + 2}$

Subtract $12$ from $0$ .

$y = \frac{- 12}{0 + 2}$

Simplify the expression.

Add $0$ and $2$ .

$y = \frac{- 12}{2}$

Divide $- 12$ by $2$ .

$y = - 6$

y-intercept(s) in point form.

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

Step 4

List the intersections.

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

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

Step 5

Find the x and y Intercepts (x^2-4x-12)/(x+2)

Related Questions

Support LCMGCF.com by disabling your adblocker.