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Popular >

range of f(x)=(x-4)^2-9

Solution

range

f (x) = (x - 4)^{2} - 9

Solution

f (x) \geq - 9

+1

Interval Notation

[- 9, \infty)

Solution steps

Vertex of

(x - 4)^{2} - 9 :

Minimum

(4, - 9)

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, - 9)

f (x) \geq - 9

Popular Examples

intercepts of (3x-8)/(2x+1)intercepts

\frac{3 x - 8}{2 x + 1}

perpendicular y= 5/2 x-8 perpendicular

y = \frac{5}{2} x - 8

asymptotes of f(x)=(x^2-5x+3)/(x-3)asymptotes

f (x) = \frac{x ^{2} - 5 x + 3}{x - 3}

asymptotes of f(x)=(2x)/(x^2-16)asymptotes

f (x) = \frac{2 x}{x ^{2} - 16}

domain of sqrt(x)*7-x domain

x \cdot 7 - x

Frequently Asked Questions (FAQ)

What is the range of f(x)=(x-4)^2-9 ?
The range of f(x)=(x-4)^2-9 is f(x)>=-9