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Popular >

range of 3x^2-6x+12

Solution

range

3 x^{2} - 6 x + 12

Solution

f (x) \geq 9

+1

Interval Notation

[9, \infty)

Solution steps

Vertex of

3 x^{2} - 6 x + 12 :

Minimum

(1, 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 = 3,

Vertex

(x_{v}, y_{v}) = (1, 9)

f (x) \geq 9

Popular Examples

symmetry y=x^3+10x symmetry

y = x^{3} + 10 x

domain of f(x)= 1/(x^2-8x-9)domain

f (x) = \frac{1}{x ^{2} - 8 x - 9}

range of f(x)=5x-12 range

f (x) = 5 x - 12

extreme f(x)=3x^4-28x^3+60x^2 extreme points

f (x) = 3 x^{4} - 28 x^{3} + 60 x^{2}

distance (2,7),(8,9)distance

(2, 7), (8, 9)

Frequently Asked Questions (FAQ)

What is the range of 3x^2-6x+12 ?
The range of 3x^2-6x+12 is f(x)>= 9