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Popular >

range of y=-x^2+2x+3

Solution

range

y = - 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

asymptotes of (8x-8)/(x+2)asymptotes

\frac{8 x - 8}{x + 2}

domain of f(x)=sqrt(2x+9)domain

f (x) = 2 x + 9

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

\frac{x ^{2} + x - 1}{x}

distance (1,0),(1,-4)distance

(1, 0), (1, - 4)

domain of (x/(x+2))/(x/(x+2)+2)domain

\frac{\frac{x}{x + 2}}{\frac{x}{x + 2} + 2}

Frequently Asked Questions (FAQ)

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