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Popular >

range of 4x^2-x+17

Solution

range

4 x^{2} - x + 17

Solution

f (x) \geq \frac{271}{16}

+1

Interval Notation

[\frac{271}{16}, \infty)

Solution steps

Vertex of

4 x^{2} - x + 17 :

Minimum

(\frac{1}{8}, \frac{271}{16})

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 = 4,

Vertex

(x_{v}, y_{v}) = (\frac{1}{8}, \frac{271}{16})

f (x) \geq \frac{271}{16}

Popular Examples

inflection 3x^3-36x-5 inflection points

3 x^{3} - 36 x - 5

range of f(x)=log_{10}(1/x)range

f (x) = lo g_{10} (\frac{1}{x})

monotone-2x^2+2x monotone intervals

- 2 x^{2} + 2 x

monotone (sqrt(1-x^2))/(2x+1)monotone intervals

\frac{1 - x ^{2}}{2 x + 1}

inflection x^3+8 inflection points

x^{3} + 8

Frequently Asked Questions (FAQ)

What is the range of 4x^2-x+17 ?
The range of 4x^2-x+17 is f(x)>= 271/16