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Popular Functions >

range of f(x)=-(x+3)^2+4

Solution

range

f (x) = - (x + 3)^{2} + 4

Solution

f (x) \leq 4

+1

Interval Notation

(- \infty, 4]

Solution steps

Vertex of

- (x + 3)^{2} + 4 :

Maximum

(- 3, 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}) = (- 3, 4)

f (x) \leq 4

Graph

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Frequently Asked Questions (FAQ)

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