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Popular >

range of f(x)=3(x-6)^2+1

Solution

range

f (x) = 3 (x - 6)^{2} + 1

Solution

f (x) \geq 1

+1

Solution steps

Vertex of

3 (x - 6)^{2} + 1 :

Minimum

(6, 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 = 3,

Vertex

(x_{v}, y_{v}) = (6, 1)

f (x) \geq 1

Popular Examples

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

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

range of-sqrt(x+3)range

- x + 3

extreme y=x^3+y^3-x-y-2=0 extreme points

y = x^{3} + y^{3} - x - y - 2 = 0

inverse of f(x)= x/(-8x+3)inverse

f (x) = \frac{x}{- 8 x + 3}

midpoint (6,9sqrt(7)),(-4,-7sqrt(7))midpoint

(6, 97), (- 4, - 77)

Frequently Asked Questions (FAQ)

What is the range of f(x)=3(x-6)^2+1 ?
The range of f(x)=3(x-6)^2+1 is f(x)>= 1