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Popular >

range of g(x)=5x^2-2x+1

Solution

range

g (x) = 5 x^{2} - 2 x + 1

Solution

f (x) \geq \frac{4}{5}

+1

Interval Notation

[\frac{4}{5}, \infty)

Solution steps

Vertex of

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

Minimum

(\frac{1}{5}, \frac{4}{5})

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 = 5,

Vertex

(x_{v}, y_{v}) = (\frac{1}{5}, \frac{4}{5})

f (x) \geq \frac{4}{5}

Popular Examples

shift cos(x-pi/2)shift

cos (x - \frac{π}{2})

inverse of f(x)=((x-4))/(3x+5)inverse

f (x) = \frac{( x - 4 )}{3 x + 5}

asymptotes of (15x^2)/(x+5)asymptotes

\frac{15 x ^{2}}{x + 5}

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

inverse of f(x)=sqrt(x^2-4x)inverse

f (x) = x^{2} - 4 x

Frequently Asked Questions (FAQ)

What is the range of g(x)=5x^2-2x+1 ?
The range of g(x)=5x^2-2x+1 is f(x)>= 4/5