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Popular >

range of x^2-4x

Solution

range

x^{2} - 4 x

Solution

f (x) \geq - 4

+1

Interval Notation

[- 4, \infty)

Solution steps

Vertex of

x^{2} - 4 x :

Minimum

(2, - 4)

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, - 4)

f (x) \geq - 4

Popular Examples

intercepts of f(x)=2x^3+15x^2+7x intercepts

f (x) = 2 x^{3} + 15 x^{2} + 7 x

inverse of 3sin(x)inverse

3 sin (x)

line 4y+16=0 line

4 y + 16 = 0

range of f(x)=2x^2-4x-1 range

f (x) = 2 x^{2} - 4 x - 1

inverse of x^2-6x+11 inverse

x^{2} - 6 x + 11

Frequently Asked Questions (FAQ)

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