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Popular >

range of f(x)=4x^2-8x-1

Solution

range

f (x) = 4 x^{2} - 8 x - 1

Solution

f (x) \geq - 5

+1

Interval Notation

[- 5, \infty)

Solution steps

Vertex of

4 x^{2} - 8 x - 1 :

Minimum

(1, - 5)

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 = 4,

Vertex

(x_{v}, y_{v}) = (1, - 5)

f (x) \geq - 5

Popular Examples

asymptotes of f(x)=a^x asymptotes

f (x) = a^{x}

domain of f(x)=12x+29 domain

f (x) = 12 x + 29

line (-1x)/3+2/1+(5x)/2-6/1 line

\frac{- 1 x}{3} + \frac{2}{1} + \frac{5 x}{2} - \frac{6}{1}

symmetry y=x^2-2x-5 symmetry

y = x^{2} - 2 x - 5

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

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

Frequently Asked Questions (FAQ)

What is the range of f(x)=4x^2-8x-1 ?
The range of f(x)=4x^2-8x-1 is f(x)>=-5