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Popular >

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

Solution

range

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

Solution

f (x) \geq \frac{7}{4}

+1

Interval Notation

[\frac{7}{4}, \infty)

Solution steps

Vertex of

x^{2} - x + 2 :

Minimum

(\frac{1}{2}, \frac{7}{4})

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 = 1,

Vertex

(x_{v}, y_{v}) = (\frac{1}{2}, \frac{7}{4})

f (x) \geq \frac{7}{4}

Popular Examples

range of 2+1/x range

2 + \frac{1}{x}

amplitude of-1/3 cos(3x)amplitude

- \frac{1}{3} cos (3 x)

slope of y= 1/3 x-5 slope

y = \frac{1}{3} x - 5

inverse of f(x)= 4/5 x+1 inverse

f (x) = \frac{4}{5} x + 1

range of (2x+3)/(x-2)range

\frac{2 x + 3}{x - 2}

Frequently Asked Questions (FAQ)

What is the range of f(x)=x^2-x+2 ?
The range of f(x)=x^2-x+2 is f(x)>= 7/4