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Popular >

range of (3-2x)(12-x)

Solution

range

(3 - 2 x) (12 - x)

Solution

f (x) \geq - \frac{441}{8}

+1

Interval Notation

[- \frac{441}{8}, \infty)

Solution steps

Vertex of

(3 - 2 x) (12 - x) :

Minimum

(\frac{27}{4}, - \frac{441}{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{27}{4}, - \frac{441}{8})

f (x) \geq - \frac{441}{8}

Popular Examples

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

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

domain of f(x)=(1-6sqrt(x))/x domain

f (x) = \frac{1 - 6 x}{x}

inflection f(x)=x^{2/3}-3 inflection points

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

inverse of 7x+2 inverse

7 x + 2

domain of f(10)= 1/(sqrt(x-1))domain

f (10) = \frac{1}{x - 1}

Frequently Asked Questions (FAQ)

What is the range of (3-2x)(12-x) ?
The range of (3-2x)(12-x) is f(x)>=-441/8