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Popular >

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

Solution

range

y = - \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

inflection cot(x-pi)-2 inflection points

cot (x - π) - 2

f (x) = \frac{1}{2} x^{3}

inverse of f(x)=(-15+4x)/3 inverse

f (x) = \frac{- 15 + 4 x}{3}

domain of f(x)=(sqrt(7+x))/(8-x)domain

f (x) = \frac{7 + x}{8 - x}

intercepts of sqrt(X+3)intercepts

X + 3

Frequently Asked Questions (FAQ)

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