en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

range

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

Solution

f (x) \geq - \frac{25}{4}

+1

Interval Notation

[- \frac{25}{4}, \infty)

Solution steps

Vertex of

x^{2} - 3 x - 4 :

Minimum

(\frac{3}{2}, - \frac{25}{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}) = (\frac{3}{2}, - \frac{25}{4})

f (x) \geq - \frac{25}{4}

Popular Examples

extreme f(x)=x^2+((26-2x)^2)/9 extreme points

f (x) = x^{2} + \frac{( 26 - 2 x ) ^{2}}{9}

critical f(x)=1 critical points

f (x) = 1

extreme f(x)=(3x)/(9-x^2)extreme points

f (x) = \frac{3 x}{9 - x ^{2}}

inverse of f(x)=(x+5)^2-2 inverse

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

extreme f(x)=3xsqrt(5-x)extreme points

f (x) = 3 x 5 - x

Frequently Asked Questions (FAQ)

What is the range of f(x)=x^2-3x-4 ?
The range of f(x)=x^2-3x-4 is f(x)>=-25/4