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Popular >

range of 2(x-4)^2+3

Solution

range

2 (x - 4)^{2} + 3

Solution

f (x) \geq 3

+1

Interval Notation

[3, \infty)

Solution steps

Vertex of

2 (x - 4)^{2} + 3 :

Minimum

(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 = 2,

Vertex

(x_{v}, y_{v}) = (4, 3)

f (x) \geq 3

Popular Examples

extreme f(x)=(10)/(x^2+1)extreme points

f (x) = \frac{10}{x ^{2} + 1}

amplitude of 8cos(x)amplitude

8 cos (x)

domain of f(x)=ln(16x)domain

f (x) = ln (16 x)

domain of f(x)=(x-2)/(x+1)domain

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

domain of 2x^2-3x+1 domain

2 x^{2} - 3 x + 1

Frequently Asked Questions (FAQ)

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