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Popular Functions >

range of f(x)=-1/2 x^2-4x+10

Solution

range

f (x) = - \frac{1}{2} x^{2} - 4 x + 10

Solution

f (x) \leq 18

+1

Interval Notation

(- \infty, 18]

Solution steps

Vertex of

- \frac{1}{2} x^{2} - 4 x + 10 :

Maximum

(- 4, 18)

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}) = (- 4, 18)

f (x) \leq 18

Graph

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Frequently Asked Questions (FAQ)

What is the range of f(x)=-1/2 x^2-4x+10 ?
The range of f(x)=-1/2 x^2-4x+10 is f(x)<= 18