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Popular >

range of f(x)=3x^2-x-3

Solution

range

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

Solution

f (x) \geq - \frac{37}{12}

+1

Interval Notation

[- \frac{37}{12}, \infty)

Solution steps

Vertex of

3 x^{2} - x - 3 :

Minimum

(\frac{1}{6}, - \frac{37}{12})

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}) = (\frac{1}{6}, - \frac{37}{12})

f (x) \geq - \frac{37}{12}

Popular Examples

intercepts of f(x)=4x^2+8x-11 intercepts

f (x) = 4 x^{2} + 8 x - 11

range of f(x)=(6x-6)/(x+2)range

f (x) = \frac{6 x - 6}{x + 2}

asymptotes of f(x)=sin(x)asymptotes

f (x) = sin (x)

domain of f(x)= 1/(sqrt(|x^3-x|))domain

f (x) = \frac{1}{∣ x ^{3} - x ∣}

domain of f(x)= 1/(8x-24)domain

f (x) = \frac{1}{8 x - 24}

Frequently Asked Questions (FAQ)

What is the range of f(x)=3x^2-x-3 ?
The range of f(x)=3x^2-x-3 is f(x)>=-37/12