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Popular >

range of y=-3x^2-12x-9

Solution

range

y = - 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

range of y=1+3/(x-1)range

y = 1 + \frac{3}{x - 1}

intercepts of f(x)=x-3y=-3 intercepts

f (x) = x - 3 y = - 3

critical f(x)=x^{1/11}(x-1)^2 critical points

f (x) = x^{\frac{1}{11}} (x - 1)^{2}

extreme f(x)= 1/3 x^3+x^2-3x extreme points

f (x) = \frac{1}{3} x^{3} + x^{2} - 3 x

range of (2x+3)/(x(x^2+2x-3))range

\frac{2 x + 3}{x ( x ^{2} + 2 x - 3 )}

Frequently Asked Questions (FAQ)

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