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Popular >

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

Solution

range

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

Solution

f (x) \geq - 3

+1

Interval Notation

[- 3, \infty)

Solution steps

Vertex of

2 (x - 2)^{2} - 3 :

Minimum

(2, - 3)

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 = 2,

Vertex

(x_{v}, y_{v}) = (2, - 3)

f (x) \geq - 3

Popular Examples

distance (-3,0),(-7,-5)distance

(- 3, 0), (- 7, - 5)

domain of (x/(2x^2-5))/(sqrt(x))domain

\frac{\frac{x}{2 x ^{2} - 5}}{x}

critical f(x)=x^3+3x^2-72x critical points

f (x) = x^{3} + 3 x^{2} - 72 x

inverse of 8x^4-8x^2+1 inverse

8 x^{4} - 8 x^{2} + 1

domain of 1 domain

1

Frequently Asked Questions (FAQ)

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