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Popular >

range of 4x^2-8x+3

Solution

range

4 x^{2} - 8 x + 3

Solution

f (x) \geq - 1

+1

Interval Notation

[- 1, \infty)

Solution steps

Vertex of

4 x^{2} - 8 x + 3 :

Minimum

(1, - 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 = 4,

Vertex

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

f (x) \geq - 1

Popular Examples

domain of f(x)=(-9x+2)/(x+7)domain

f (x) = \frac{- 9 x + 2}{x + 7}

extreme f(x)=x^3+3x+5 extreme points

f (x) = x^{3} + 3 x + 5

inverse of f(x)=2^{3x-1}inverse

f (x) = 2^{3 x - 1}

asymptotes of f(x)= 2/(x-3)-1 asymptotes

f (x) = \frac{2}{x - 3} - 1

inverse of f(x)=13x+10 inverse

f (x) = 13 x + 10

Frequently Asked Questions (FAQ)

What is the range of 4x^2-8x+3 ?
The range of 4x^2-8x+3 is f(x)>=-1