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Popular >

range of x^2+6x+3

Solution

range

x^{2} + 6 x + 3

Solution

f (x) \geq - 6

+1

Interval Notation

[- 6, \infty)

Solution steps

Vertex of

x^{2} + 6 x + 3 :

Minimum

(- 3, - 6)

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}) = (- 3, - 6)

f (x) \geq - 6

Popular Examples

perpendicular y=-1/3 x-2,(1,3)perpendicular

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

line-4x+6y+1=0 line

- 4 x + 6 y + 1 = 0

extreme f(x)= 8/(x^2+4)extreme points

f (x) = \frac{8}{x ^{2} + 4}

intercepts of f(x)=-2x^2+8x intercepts

f (x) = - 2 x^{2} + 8 x

range of sqrt(6x-3)range

6 x - 3

Frequently Asked Questions (FAQ)

What is the range of x^2+6x+3 ?
The range of x^2+6x+3 is f(x)>=-6