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Popular >

range of f(x)=(x+4)^2-9

Solution

range

f (x) = (x + 4)^{2} - 9

Solution

f (x) \geq - 9

+1

Interval Notation

[- 9, \infty)

Solution steps

Vertex of

(x + 4)^{2} - 9 :

Minimum

(- 4, - 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}) = (- 4, - 9)

f (x) \geq - 9

Popular Examples

extreme f(x)=x(75-3x)extreme points

f (x) = x (75 - 3 x)

range of (x^2-3x-2)/(x^2-4)range

\frac{x ^{2} - 3 x - 2}{x ^{2} - 4}

slope of y=-6/7 x slope

y = - \frac{6}{7} x

intercepts of f(x)=(x^2+8x-9)/(x^2+3x-4)intercepts

f (x) = \frac{x ^{2} + 8 x - 9}{x ^{2} + 3 x - 4}

inverse of x^3-5 inverse

x^{3} - 5

Frequently Asked Questions (FAQ)

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