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Popular >

range of-(x+5)^2+2

Solution

range

- (x + 5)^{2} + 2

Solution

f (x) \leq 2

+1

Interval Notation

(- \infty, 2]

Solution steps

Vertex of

- (x + 5)^{2} + 2 :

Maximum

(- 5, 2)

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}) = (- 5, 2)

f (x) \leq 2

Popular Examples

extreme y=x^4-16x^2 extreme points

y = x^{4} - 16 x^{2}

domain of f(x)=3x^2-8 domain

f (x) = 3 x^{2} - 8

monotone (x^2+2x+4)/(x-2)monotone intervals

\frac{x ^{2} + 2 x + 4}{x - 2}

domain of h(x)=(x^2-8x+15)/(x^2-10x+21)domain

h (x) = \frac{x ^{2} - 8 x + 15}{x ^{2} - 10 x + 21}

monotone f(x)=x^2+4x-5 monotone intervals

f (x) = x^{2} + 4 x - 5

Frequently Asked Questions (FAQ)

What is the range of-(x+5)^2+2 ?
The range of-(x+5)^2+2 is f(x)<= 2