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Popular >

range of 3x^2+2x-1

Solution

range

3 x^{2} + 2 x - 1

Solution

f (x) \geq - \frac{4}{3}

+1

Interval Notation

[- \frac{4}{3}, \infty)

Solution steps

Vertex of

3 x^{2} + 2 x - 1 :

Minimum

(- \frac{1}{3}, - \frac{4}{3})

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}) = (- \frac{1}{3}, - \frac{4}{3})

f (x) \geq - \frac{4}{3}

Popular Examples

extreme f(x)=2x^3-3x^2-72x-12 extreme points

f (x) = 2 x^{3} - 3 x^{2} - 72 x - 12

domain of sqrt(15-5x)domain

15 - 5 x

symmetry 3x^2-12x+11 symmetry

3 x^{2} - 12 x + 11

inverse of f(x)= 5/2 x-2 inverse

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

inflection (-2)/(x^2)inflection points

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

Frequently Asked Questions (FAQ)

What is the range of 3x^2+2x-1 ?
The range of 3x^2+2x-1 is f(x)>=-4/3