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Popular >

range of f(x)=x^2+4x-5

Solution

range

f (x) = x^{2} + 4 x - 5

Solution

f (x) \geq - 9

+1

Interval Notation

[- 9, \infty)

Solution steps

Vertex of

x^{2} + 4 x - 5 :

Minimum

(- 2, - 9)

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, - 9)

f (x) \geq - 9

Popular Examples

symmetry (x-2)^2-1 symmetry

(x - 2)^{2} - 1

inverse of f(x)=(3x-4)/(5x+3)inverse

f (x) = \frac{3 x - 4}{5 x + 3}

intercepts of x^3-7x+6 intercepts

x^{3} - 7 x + 6

extreme f(x)=-x^3+3x^2-4 extreme points

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

domain of f(x)=2+1/x domain

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

Frequently Asked Questions (FAQ)

What is the range of f(x)=x^2+4x-5 ?
The range of f(x)=x^2+4x-5 is f(x)>=-9