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Popular >

range of f(x)= 1/2 (x-3)^2+4

Solution

range

f (x) = \frac{1}{2} (x - 3)^{2} + 4

Solution

f (x) \geq 4

+1

Interval Notation

[4, \infty)

Solution steps

Vertex of

\frac{1}{2} (x - 3)^{2} + 4 :

Minimum

(3, 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 = \frac{1}{2},

Vertex

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

f (x) \geq 4

Popular Examples

intercepts of f(x)=-2x-1 intercepts

f (x) = - 2 x - 1

domain of 2x^2+24x+76 domain

2 x^{2} + 24 x + 76

inverse of f(x)=5-1/5 x inverse

f (x) = 5 - \frac{1}{5} x

domain of f(x)=(3+x)/(sqrt(x+2))domain

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

distance (x,-4),(-4,-1)distance

(x, - 4), (- 4, - 1)

Frequently Asked Questions (FAQ)

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