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Popular >

y=(2x^2+5x+2)/(x^2-4x+3)

Solution

y = \frac{2 x ^{2} + 5 x + 2}{x ^{2} - 4 x + 3}

Solution

Domain : x < 1 or 1 < x < 3 or x > 3

Range : f (x) \leq - \frac{3 35}{2} - 9 or f (x) \geq \frac{3 35}{2} - 9

X Intercepts : (- \frac{1}{2}, 0), (- 2, 0), Y Intercepts : (0, \frac{2}{3})

Asymptotes : Vertical x = 1, x = 3, Horizontal y = 2

Extreme Points : Minimum (- \frac{- 4 + 3 35}{13}, - \frac{3 ( 6 - 35 )}{2}), Maximum (\frac{4 + 3 35}{13}, - \frac{3 ( 6 + 35 )}{2})

+1

Solution steps

Domain of

\frac{2 x ^{2} + 5 x + 2}{x ^{2} - 4 x + 3} : x < 1 or 1 < x < 3 or x > 3

Range of

\frac{2 x ^{2} + 5 x + 2}{x ^{2} - 4 x + 3} : f (x) \leq - \frac{3 35}{2} - 9 or f (x) \geq \frac{3 35}{2} - 9

Axis interception points of

\frac{2 x ^{2} + 5 x + 2}{x ^{2} - 4 x + 3} :

X Intercepts

: (- \frac{1}{2}, 0), (- 2, 0),

Y Intercepts

: (0, \frac{2}{3})

Asymptotes of

\frac{2 x ^{2} + 5 x + 2}{x ^{2} - 4 x + 3} :

Vertical

: x = 1, x = 3,

Horizontal

: y = 2

Extreme Points of

\frac{2 x ^{2} + 5 x + 2}{x ^{2} - 4 x + 3} :

Minimum

(- \frac{- 4 + 3 35}{13}, - \frac{3 ( 6 - 35 )}{2}),

Maximum

(\frac{4 + 3 35}{13}, - \frac{3 ( 6 + 35 )}{2})

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Frequently Asked Questions (FAQ)

What is the y=(2x^2+5x+2)/(x^2-4x+3) ?
The y=(2x^2+5x+2)/(x^2-4x+3) is