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Popular Functions >

y=-1/2 x^2+11/4 x+3/2

Solution

y = - \frac{1}{2} x^{2} + \frac{11}{4} x + \frac{3}{2}

Solution

Domain : - \infty < x < \infty

Range : f (x) \leq \frac{169}{32}

X Intercepts : (- \frac{1}{2}, 0), (6, 0), Y Intercepts : (0, \frac{3}{2})

Vertex : Maximum (\frac{11}{4}, \frac{169}{32})

Inverse : - \frac{- 11 + - 32 x + 169}{4}, - \frac{- 11 - - 32 x + 169}{4}

+1

Interval Notation

Domain : (- \infty, \infty)

Range : (- \infty, \frac{169}{32}]

Solution steps

Domain of

- \frac{1}{2} x^{2} + \frac{11}{4} x + \frac{3}{2} : - \infty < x < \infty

Range of

- \frac{1}{2} x^{2} + \frac{11}{4} x + \frac{3}{2} : f (x) \leq \frac{169}{32}

Axis interception points of

- \frac{1}{2} x^{2} + \frac{11}{4} x + \frac{3}{2} :

X Intercepts

: (- \frac{1}{2}, 0), (6, 0),

Y Intercepts

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

Vertex of

- \frac{1}{2} x^{2} + \frac{11}{4} x + \frac{3}{2} :

Maximum

(\frac{11}{4}, \frac{169}{32})

Inverse of

- \frac{1}{2} x^{2} + \frac{11}{4} x + \frac{3}{2} : - \frac{- 11 + - 32 x + 169}{4}, - \frac{- 11 - - 32 x + 169}{4}

Graph

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