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Popular Functions >

range of f(x)=-1/2 x^2+5x-2

Solution

range

f (x) = - \frac{1}{2} x^{2} + 5 x - 2

Solution

f (x) \leq \frac{21}{2}

+1

Interval Notation

(- \infty, \frac{21}{2}]

Solution steps

Vertex of

- \frac{1}{2} x^{2} + 5 x - 2 :

Maximum

(5, \frac{21}{2})

For a parabola

a x^{2} + b x + c

with Vertex

(x_{v}, y_{v})

If

a < 0

the range is

f (x) \leq y_{v}

If

a > 0

the range is

f (x) \geq y_{v}

a = - \frac{1}{2},

Vertex

(x_{v}, y_{v}) = (5, \frac{21}{2})

f (x) \leq \frac{21}{2}

Graph

Popular Examples

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domain of-x/(x-8)

line (3,-4),(-1,4)

critical f(x)=sin(pix)

Frequently Asked Questions (FAQ)

What is the range of f(x)=-1/2 x^2+5x-2 ?
The range of f(x)=-1/2 x^2+5x-2 is f(x)<= 21/2