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Popular >

range of f(x)=x^2-12x+5

Solution

range

f (x) = x^{2} - 12 x + 5

Solution

f (x) \geq - 31

+1

Interval Notation

[- 31, \infty)

Solution steps

Vertex of

x^{2} - 12 x + 5 :

Minimum

(6, - 31)

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}) = (6, - 31)

f (x) \geq - 31

Popular Examples

domain of sqrt(x+1)+1/(x^2+1)domain

x + 1 + \frac{1}{x ^{2} + 1}

slope ofintercept 4x-3y=-18 slope intercept

4 x - 3 y = - 18

inverse of f(x)=3(x^{1/2}-3)inverse

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

inverse of sqrt(x-12)inverse

x - 12

domain of f(x)=-7/(2xsqrt(x))domain

f (x) = - \frac{7}{2 x x}

Frequently Asked Questions (FAQ)

What is the range of f(x)=x^2-12x+5 ?
The range of f(x)=x^2-12x+5 is f(x)>=-31