Find the x and y Intercepts f(x)=(x^2-4x-5)/(4x+4)

$f (x) = \frac{x^{2} - 4 x - 5}{4 x + 4}$

Step 1

Find the x-intercepts.

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

$0 = \frac{x^{2} - 4 x - 5}{4 x + 4}$

Solve the equation.

Set the numerator equal to zero.

$x^{2} - 4 x - 5 = 0$

Solve the equation for $x$ .

Factor $x^{2} - 4 x - 5$ 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 $- 5$ and whose sum is $- 4$ .

$- 5, 1$

Write the factored form using these integers.

$(x - 5) (x + 1) = 0$

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

$x - 5 = 0$

$x + 1 = 0$

Set $x - 5$ equal to $0$ and solve for $x$ .

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

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.

$x = - 1$

The final solution is all the values that make $(x - 5) (x + 1) = 0$ true.

$x = 5, - 1$

Exclude the solutions that do not make $0 = \frac{x^{2} - 4 x - 5}{4 x + 4}$ true.

$x = 5$

x-intercept(s) in point form.

x-intercept(s): $(5, 0)$

Step 2

Find the y-intercepts.

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

$y = \frac{{(0)}^{2} - 4 \cdot 0 - 5}{4 (0) + 4}$

Solve the equation.

Remove parentheses.

$y = \frac{0^{2} - 4 \cdot 0 - 5}{4 (0) + 4}$

Remove parentheses.

$y = \frac{{(0)}^{2} - 4 \cdot 0 - 5}{4 (0) + 4}$

Simplify $\frac{{(0)}^{2} - 4 \cdot 0 - 5}{4 (0) + 4}$ .

Simplify the numerator.

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

$y = \frac{0 - 4 \cdot 0 - 5}{4 (0) + 4}$

Multiply $- 4$ by $0$ .

$y = \frac{0 + 0 - 5}{4 (0) + 4}$

Add $0$ and $0$ .

$y = \frac{0 - 5}{4 (0) + 4}$

Subtract $5$ from $0$ .

$y = \frac{- 5}{4 (0) + 4}$

Simplify the denominator.

Multiply $4$ by $0$ .

$y = \frac{- 5}{0 + 4}$

Add $0$ and $4$ .

$y = \frac{- 5}{4}$

Move the negative in front of the fraction.

$y = - \frac{5}{4}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{5}{4})$

Step 3

List the intersections.

x-intercept(s): $(5, 0)$

y-intercept(s): $(0, - \frac{5}{4})$

Step 4

Find the x and y Intercepts f(x)=(x^2-4x-5)/(4x+4)

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