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Popular >

range of f(x)=-3x^2-12x-9

Solution

range

f (x) = - 3 x^{2} - 12 x - 9

Solution

f (x) \leq 3

+1

Interval Notation

(- \infty, 3]

Solution steps

Vertex of

- 3 x^{2} - 12 x - 9 :

Maximum

(- 2, 3)

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 = - 3,

Vertex

(x_{v}, y_{v}) = (- 2, 3)

f (x) \leq 3

Popular Examples

asymptotes of (x^3+5)/(x^5+2)asymptotes

\frac{x ^{3} + 5}{x ^{5} + 2}

perpendicular y= 3/4 x-31/4 ,(1,0)perpendicular

y = \frac{3}{4} x - \frac{31}{4}, (1, 0)

inverse of f(x)=-(-12x+13)^2-1 inverse

f (x) = - (- 12 x + 13)^{2} - 1

domain of f(x)=(x^2-2x-48)/(x+6)domain

f (x) = \frac{x ^{2} - 2 x - 48}{x + 6}

symmetry (x+2)^2-4 symmetry

(x + 2)^{2} - 4

Frequently Asked Questions (FAQ)

What is the range of f(x)=-3x^2-12x-9 ?
The range of f(x)=-3x^2-12x-9 is f(x)<= 3