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Popular >

range of-x^2+2x+3

Solution

range

- 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

extreme f(x)=(4x-3)^{1/3}extreme points

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

inverse of f(x)=\sqrt[3]{x-2}+4 inverse

asymptotes of f(x)=(x^2-3x-70)/(3x+21)asymptotes

f (x) = \frac{x ^{2} - 3 x - 70}{3 x + 21}

inverse of f(x)=5sin(x)-7 inverse

f (x) = 5 sin (x) - 7

inverse of f(x)=5x^3-14 inverse

f (x) = 5 x^{3} - 14

Frequently Asked Questions (FAQ)

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