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Popular >

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

Solution

range

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

Solution

f (x) \geq 4

+1

Interval Notation

[4, \infty)

Solution steps

Vertex of

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

Minimum

(2, 4)

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}) = (2, 4)

f (x) \geq 4

Popular Examples

inverse of f(x)=(4-x)^3 inverse

f (x) = (4 - x)^{3}

symmetry y=x^2-8x-6 symmetry

y = x^{2} - 8 x - 6

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

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

intercepts of f(x)=-x^2+4 intercepts

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

inverse of f(x)=(2x+1)/(5x+3)inverse

f (x) = \frac{2 x + 1}{5 x + 3}

Frequently Asked Questions (FAQ)

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