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Popular >

range of f(x)=-x^2+2x-4

Solution

range

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

Solution

f (x) \leq - 3

+1

Interval Notation

(- \infty, - 3]

Solution steps

Vertex of

- x^{2} + 2 x - 4 :

Maximum

(1, - 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 = - 1,

Vertex

(x_{v}, y_{v}) = (1, - 3)

f (x) \leq - 3

Popular Examples

parallel 3x+y=5 parallel

3 x + y = 5

inverse of f(x)=((x-3))/((x+7))inverse

f (x) = \frac{( x - 3 )}{( x + 7 )}

parity (sin(3y)cot(5y))/(ycot(4y))parity

\frac{sin ( 3 y ) cot ( 5 y )}{y cot ( 4 y )}

extreme f(x)=\sqrt[3]{x+3}extreme points

monotone f(x)=1-(3/(x^2-1))monotone intervals

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

Frequently Asked Questions (FAQ)

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