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Popular >

range of f(x)=-x^2-2x+3

Solution

range

f (x) = - x^{2} - 2 x + 3

Solution

f (x) \leq 4

+1

Interval Notation

(- \infty, 4]

Solution steps

Vertex of

- x^{2} - 2 x + 3 :

Maximum

(- 1, 4)

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 = - 1,

Vertex

(x_{v}, y_{v}) = (- 1, 4)

f (x) \leq 4

Popular Examples

domain of f(x)=e^{-3t}domain

f (x) = e^{- 3 t}

midpoint (-2,-9),(-6,-1)midpoint

(- 2, - 9), (- 6, - 1)

inflection f(x)=x^4-24x^2 inflection points

f (x) = x^{4} - 24 x^{2}

extreme f(x)=x^2+8x+7 extreme points

f (x) = x^{2} + 8 x + 7

parity x^2 parity

x^{2}

Frequently Asked Questions (FAQ)

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