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Popular Functions >

range of y=x^2+2x+1

Solution

range

y = x^{2} + 2 x + 1

Solution

f (x) \geq 0

+1

Interval Notation

[0, \infty)

Solution steps

Vertex of

x^{2} + 2 x + 1 :

Minimum

(- 1, 0)

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}) = (- 1, 0)

f (x) \geq 0

Graph

Popular Examples

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range of y=(x^2)/(x^2-4)

line 4x+3x-12=0

Frequently Asked Questions (FAQ)

What is the range of y=x^2+2x+1 ?
The range of y=x^2+2x+1 is f(x)>= 0