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Popular >

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

Solution

range

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

Solution

f (x) \leq 1

+1

Interval Notation

(- \infty, 1]

Solution steps

Vertex of

- x^{2} + 4 x - 3 :

Maximum

(2, 1)

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}) = (2, 1)

f (x) \leq 1

Popular Examples

slope of 5x-2y+4 slope

5 x - 2 y + 4

critical x^2-18x-4 critical points

x^{2} - 18 x - 4

inverse of f(x)=(-x+9)/(3+4x)inverse

f (x) = \frac{- x + 9}{3 + 4 x}

distance (6,-3),(8,8)distance

(6, - 3), (8, 8)

intercepts of f(x)=x^3+2x^2-9x-18 intercepts

f (x) = x^{3} + 2 x^{2} - 9 x - 18

Frequently Asked Questions (FAQ)

What is the range of f(x)=-x^2+4x-3 ?
The range of f(x)=-x^2+4x-3 is f(x)<= 1