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Popular Functions >

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}

Graph

Popular Examples

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monotone-2x^2+2x

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

perpendicular x=1

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