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Popular >

range of f(x)=-1/3 x^2+4x+11

Solution

range

f (x) = - \frac{1}{3} x^{2} + 4 x + 11

Solution

f (x) \leq 23

+1

Interval Notation

(- \infty, 23]

Solution steps

Vertex of

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

Maximum

(6, 23)

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}{3},

Vertex

(x_{v}, y_{v}) = (6, 23)

f (x) \leq 23

Popular Examples

slope ofintercept x-7=3 slope intercept

x - 7 = 3

asymptotes of x/((x-1)^2)asymptotes

\frac{x}{( x - 1 ) ^{2}}

inverse of f(v)=9+sqrt(2v-3)inverse

f (v) = 9 + 2 v - 3

parity f(x)=-7x^4-x^2 parity

f (x) = - 7 x^{4} - x^{2}

inverse of f(x)= 1/2 ln((1+x)/(1-x))inverse

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

Frequently Asked Questions (FAQ)

What is the range of f(x)=-1/3 x^2+4x+11 ?
The range of f(x)=-1/3 x^2+4x+11 is f(x)<= 23