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Popular Functions >

range of (3-2x)(6-x)

Solution

range

(3 - 2 x) (6 - x)

Solution

f (x) \geq - \frac{81}{8}

+1

Interval Notation

Solution steps

Vertex of

(3 - 2 x) (6 - x) :

Minimum

(\frac{15}{4}, - \frac{81}{8})

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}) = (\frac{15}{4}, - \frac{81}{8})

f (x) \geq - \frac{81}{8}

Graph

Popular Examples

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

f (x) = - 2 x + 2

inverse of y=(e^x)/(1+6e^x)inverse

y = \frac{e ^{x}}{1 + 6 e ^{x}}

inverse of f(x)=sqrt((x-5))inverse

f (x) = (x - 5)

asymptotes of f(x)=log_{3}(x-1)+2 asymptotes

f (x) = lo g_{3} (x - 1) + 2

midpoint (a,2b),(2a,b-2)midpoint

(a, 2 b), (2 a, b - 2)

Frequently Asked Questions (FAQ)

What is the range of (3-2x)(6-x) ?
The range of (3-2x)(6-x) is f(x)>=-81/8