Find the x and y Intercepts y=(x^2+11x+18)/(2x+1)

$y = \frac{x^{2} + 11 x + 18}{2 x + 1}$

Step 1

Find the x-intercepts.

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

$0 = \frac{x^{2} + 11 x + 18}{2 x + 1}$

Solve the equation.

Set the numerator equal to zero.

$x^{2} + 11 x + 18 = 0$

Solve the equation for $x$ .

Factor $x^{2} + 11 x + 18$ 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 $18$ and whose sum is $11$ .

$2, 9$

Write the factored form using these integers.

$(x + 2) (x + 9) = 0$

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

$x + 2 = 0$

$x + 9 = 0$

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.

$x = - 2$

Set $x + 9$ equal to $0$ and solve for $x$ .

Set $x + 9$ equal to $0$ .

$x + 9 = 0$

Subtract $9$ from both sides of the equation.

$x = - 9$

The final solution is all the values that make $(x + 2) (x + 9) = 0$ true.

$x = - 2, - 9$

x-intercept(s) in point form.

x-intercept(s): $(- 2, 0), (- 9, 0)$

Step 2

Find the y-intercepts.

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

$y = \frac{{(0)}^{2} + 11 (0) + 18}{2 (0) + 1}$

Solve the equation.

Remove parentheses.

$y = \frac{0^{2} + 11 (0) + 18}{2 (0) + 1}$

Remove parentheses.

$y = \frac{{(0)}^{2} + 11 (0) + 18}{2 (0) + 1}$

Simplify $\frac{{(0)}^{2} + 11 (0) + 18}{2 (0) + 1}$ .

Simplify the numerator.

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

$y = \frac{0 + 11 (0) + 18}{2 (0) + 1}$

Multiply $11$ by $0$ .

$y = \frac{0 + 0 + 18}{2 (0) + 1}$

Add $0$ and $0$ .

$y = \frac{0 + 18}{2 (0) + 1}$

Add $0$ and $18$ .

$y = \frac{18}{2 (0) + 1}$

Simplify the denominator.

Multiply $2$ by $0$ .

$y = \frac{18}{0 + 1}$

Add $0$ and $1$ .

$y = \frac{18}{1}$

Divide $18$ by $1$ .

$y = 18$

y-intercept(s) in point form.

y-intercept(s): $(0, 18)$

Step 3

List the intersections.

x-intercept(s): $(- 2, 0), (- 9, 0)$

y-intercept(s): $(0, 18)$

Step 4

Find the x and y Intercepts y=(x^2+11x+18)/(2x+1)

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