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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 sqrt((6+x)/(6-x))domain

\frac{6 + x}{6 - x}

periodicity of f(x)=3cos(2x)-4 periodicity

f (x) = 3 cos (2 x) - 4

line (5,6),(1,2)line

(5, 6), (1, 2)

inverse of f(x)=\sqrt[3]{x-4}+3 inverse

perpendicular 1/2 x-y=-2,(2,4)perpendicular

\frac{1}{2} x - y = - 2, (2, 4)

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