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Popular >

range of 2x^2-3x+1

Solution

range

2 x^{2} - 3 x + 1

Solution

f (x) \geq - \frac{1}{8}

+1

Interval Notation

[- \frac{1}{8}, \infty)

Solution steps

Vertex of

2 x^{2} - 3 x + 1 :

Minimum

(\frac{3}{4}, - \frac{1}{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{3}{4}, - \frac{1}{8})

f (x) \geq - \frac{1}{8}

Popular Examples

slope of 8x-7y=15 slope

8 x - 7 y = 15

f(x)= 1/(sqrt(x))

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

domain of f(x)= 2/3-1 domain

f (x) = \frac{2}{3} - 1

range of 2sqrt(x-2)range

2 x - 2

f(θ)=sin(θ)cos(θ)

f (θ) = sin (θ) cos (θ)

Frequently Asked Questions (FAQ)

What is the range of 2x^2-3x+1 ?
The range of 2x^2-3x+1 is f(x)>=-1/8