Find the x and y Intercepts f(x)=(x-4)/(3x^2+39x+90)

$f (x) = \frac{x - 4}{3 x^{2} + 39 x + 90}$

Step 1

Find the x-intercepts.

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

$0 = \frac{x - 4}{3 x^{2} + 39 x + 90}$

Solve the equation.

Set the numerator equal to zero.

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

x-intercept(s) in point form.

x-intercept(s): $(4, 0)$

Step 2

Find the y-intercepts.

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

$y = \frac{(0) - 4}{3 {(0)}^{2} + 39 (0) + 90}$

Solve the equation.

Remove parentheses.

$y = \frac{0 - 4}{3 {(0)}^{2} + 39 (0) + 90}$

Remove parentheses.

$y = \frac{0 - 4}{3 \cdot 0^{2} + 39 (0) + 90}$

Remove parentheses.

$y = \frac{(0) - 4}{3 {(0)}^{2} + 39 (0) + 90}$

Simplify $\frac{(0) - 4}{3 {(0)}^{2} + 39 (0) + 90}$ .

Subtract $4$ from $0$ .

$y = \frac{- 4}{3 \cdot 0^{2} + 39 (0) + 90}$

Simplify the denominator.

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

$y = \frac{- 4}{3 \cdot 0 + 39 (0) + 90}$

Multiply $3$ by $0$ .

$y = \frac{- 4}{0 + 39 (0) + 90}$

Multiply $39$ by $0$ .

$y = \frac{- 4}{0 + 0 + 90}$

Add $0$ and $0$ .

$y = \frac{- 4}{0 + 90}$

Add $0$ and $90$ .

$y = \frac{- 4}{90}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 4$ and $90$ .

Factor $2$ out of $- 4$ .

$y = \frac{2 (- 2)}{90}$

Cancel the common factors.

Factor $2$ out of $90$ .

$y = \frac{2 \cdot - 2}{2 \cdot 45}$

Cancel the common factor.

$y = \frac{2 \cdot - 2}{2 \cdot 45}$

Rewrite the expression.

$y = \frac{- 2}{45}$

Move the negative in front of the fraction.

$y = - \frac{2}{45}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{2}{45})$

Step 3

List the intersections.

x-intercept(s): $(4, 0)$

y-intercept(s): $(0, - \frac{2}{45})$

Step 4

Find the x and y Intercepts f(x)=(x-4)/(3x^2+39x+90)

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