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Popular >

range of x^2+3x+3

Solution

range

x^{2} + 3 x + 3

Solution

f (x) \geq \frac{3}{4}

+1

Interval Notation

[\frac{3}{4}, \infty)

Solution steps

Vertex of

x^{2} + 3 x + 3 :

Minimum

(- \frac{3}{2}, \frac{3}{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{3}{2}, \frac{3}{4})

f (x) \geq \frac{3}{4}

Popular Examples

distance (2,3),(5,9)distance

(2, 3), (5, 9)

monotone x^3-12x^2+45x-50 monotone intervals

x^{3} - 12 x^{2} + 45 x - 50

domain of f(x)=sqrt(2x^2-5x)domain

f (x) = 2 x^{2} - 5 x

range of f(x)=4-2sqrt(x)range

f (x) = 4 - 2 x

domain of f(x)=4x^2+5x-3 domain

f (x) = 4 x^{2} + 5 x - 3

Frequently Asked Questions (FAQ)

What is the range of x^2+3x+3 ?
The range of x^2+3x+3 is f(x)>= 3/4