Find the x and y Intercepts f(x)=(x^2+3x+2)/(-4x-16)

$f (x) = \frac{x^{2} + 3 x + 2}{- 4 x - 16}$

Find the x-intercepts.

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

$0 = \frac{x^{2} + 3 x + 2}{- 4 x - 16}$

Solve the equation.

Set the numerator equal to zero.

$x^{2} + 3 x + 2 = 0$

Solve the equation for $x$ .

Factor $x^{2} + 3 x + 2$ 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 $2$ and whose sum is $3$ .

$1, 2$

Write the factored form using these integers.

$(x + 1) (x + 2) = 0$

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

$x + 1 = 0$

$x + 2 = 0$

Set $x + 1$ equal to $0$ and solve for $x$ .

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

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 $(x + 1) (x + 2) = 0$ true.

$x = - 1, - 2$

x-intercept(s) in point form.

x-intercept(s): $(- 1, 0), (- 2, 0)$

Find the y-intercepts.

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

$y = \frac{{(0)}^{2} + 3 (0) + 2}{- 4 \cdot 0 - 16}$

Solve the equation.

Remove parentheses.

$y = \frac{0^{2} + 3 (0) + 2}{- 4 \cdot 0 - 16}$

Remove parentheses.

$y = \frac{{(0)}^{2} + 3 (0) + 2}{- 4 \cdot 0 - 16}$

Simplify $\frac{{(0)}^{2} + 3 (0) + 2}{- 4 \cdot 0 - 16}$ .

Simplify the numerator.

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

$y = \frac{0 + 3 (0) + 2}{- 4 \cdot 0 - 16}$

Multiply $3$ by $0$ .

$y = \frac{0 + 0 + 2}{- 4 \cdot 0 - 16}$

Add $0$ and $0$ .

$y = \frac{0 + 2}{- 4 \cdot 0 - 16}$

Add $0$ and $2$ .

$y = \frac{2}{- 4 \cdot 0 - 16}$

Simplify the denominator.

Multiply $- 4$ by $0$ .

$y = \frac{2}{0 - 16}$

Subtract $16$ from $0$ .

$y = \frac{2}{- 16}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $2$ and $- 16$ .

Factor $2$ out of $2$ .

$y = \frac{2 (1)}{- 16}$

Cancel the common factors.

Factor $2$ out of $- 16$ .

$y = \frac{2 \cdot 1}{2 \cdot - 8}$

Cancel the common factor.

$y = \frac{2 \cdot 1}{2 \cdot - 8}$

Rewrite the expression.

$y = \frac{1}{- 8}$

Move the negative in front of the fraction.

$y = - \frac{1}{8}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{1}{8})$

List the intersections.

x-intercept(s): $(- 1, 0), (- 2, 0)$

y-intercept(s): $(0, - \frac{1}{8})$

Find the x and y Intercepts f(x)=(x^2+3x+2)/(-4x-16)

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