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Popular >

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

Solution

range

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

Solution

f (x) \geq - 1

+1

Interval Notation

[- 1, \infty)

Solution steps

Vertex of

2 (x - 2)^{2} - 1 :

Minimum

(2, - 1)

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, - 1)

f (x) \geq - 1

Popular Examples

slope ofintercept y=-3/10 x-8y slope intercept

y = - \frac{3}{10} x - 8 y

slope ofintercept-2x+6y=-12 slope intercept

- 2 x + 6 y = - 12

domain of f(x)=6-5x domain

f (x) = 6 - 5 x

simplify (4.9)(10.9)simplify

(4.9) (10.9)

symmetry y=x^2-6x symmetry

y = x^{2} - 6 x

Frequently Asked Questions (FAQ)

What is the range of f(x)=2(x-2)^2-1 ?
The range of f(x)=2(x-2)^2-1 is f(x)>=-1