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Popular >

range of (x-4)^2-1

Solution

range

(x - 4)^{2} - 1

Solution

f (x) \geq - 1

+1

Interval Notation

[- 1, \infty)

Solution steps

Vertex of

(x - 4)^{2} - 1 :

Minimum

(4, - 1)

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}) = (4, - 1)

f (x) \geq - 1

Popular Examples

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

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

inverse of f(x)=(3xsqrt(x))/8 inverse

f (x) = \frac{3 x x}{8}

inverse of f(x)=sqrt(-x)-4 inverse

f (x) = - x - 4

critical x^8(x-4)^7 critical points

x^{8} (x - 4)^{7}

inverse of y=3^x inverse

y = 3^{x}

Frequently Asked Questions (FAQ)

What is the range of (x-4)^2-1 ?
The range of (x-4)^2-1 is f(x)>=-1