Finite Math Examples

$x = - \frac{b}{2 a}$

Step 1

Find where the expression $- \frac{b}{2 a}$ is undefined.

$b = 0$

Step 2

The vertical asymptotes occur at areas of infinite discontinuity.

No Vertical Asymptotes

Step 3

$x = - \frac{b}{2 a}$ is an equation of a line, which means there are no horizontal asymptotes.

No Horizontal Asymptotes

Step 4

Find the oblique asymptote using polynomial division.

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Step 4.1

Move the negative in front of the fraction.

$- \frac{b}{2 a}$

Step 4.2

Negate $b$ .

$\frac{- b}{2 a}$

Step 4.3

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of $0$ .

$2 a$

$b$

$0$

Step 4.4

Divide the highest order term in the dividend $- b$ by the highest order term in divisor $2 a$ .

		-	$\frac{b}{2 a}$
	$2 a$	-	$b$	+	$0$

Step 4.5

Multiply the new quotient term by the divisor.

	-	$\frac{b}{2 a}$
$2 a$	-	$b$	+	$0$
	-	$b$

Step 4.6

The expression needs to be subtracted from the dividend, so change all the signs in $- b$

	-	$\frac{b}{2 a}$
$2 a$	-	$b$	+	$0$
	+	$b$

Step 4.7

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

	-	$\frac{b}{2 a}$
$2 a$	-	$b$	+	$0$
	+	$b$
		$0$

Step 4.8

Pull the next terms from the original dividend down into the current dividend.

	-	$\frac{b}{2 a}$
$2 a$	-	$b$	+	$0$
	+	$b$
		$0$	+	$0$

Step 4.9

Since the remander is $0$ , the final answer is the quotient.

$- \frac{b}{2 a}$

Step 4.10

Since there is no polynomial portion from the polynomial division, there are no oblique asymptotes.

No Oblique Asymptotes

Step 5

This is the set of all asymptotes.

No Vertical Asymptotes

No Horizontal Asymptotes

No Oblique Asymptotes

Step 6