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Popular >

range of f(x)=3x^2+18x-4

Solution

range

f (x) = 3 x^{2} + 18 x - 4

Solution

f (x) \geq - 31

+1

Interval Notation

[- 31, \infty)

Solution steps

Vertex of

3 x^{2} + 18 x - 4 :

Minimum

(- 3, - 31)

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 = 3,

Vertex

(x_{v}, y_{v}) = (- 3, - 31)

f (x) \geq - 31

Popular Examples

extreme f(x)= 1/(x+6)extreme points

f (x) = \frac{1}{x + 6}

intercepts of f(x)=x^2+3x-28 intercepts

f (x) = x^{2} + 3 x - 28

extreme f(x)=-5x^6+x^5+2x^3+4 extreme points

f (x) = - 5 x^{6} + x^{5} + 2 x^{3} + 4

asymptotes of (sqrt(x+1))/(sqrt(x-4))asymptotes

\frac{x + 1}{x - 4}

domain of f(x)= 2/(x^2+x-12)domain

f (x) = \frac{2}{x ^{2} + x - 12}

Frequently Asked Questions (FAQ)

What is the range of f(x)=3x^2+18x-4 ?
The range of f(x)=3x^2+18x-4 is f(x)>=-31