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Popular >

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

Solution

range

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

Solution

f (x) \geq 1

+1

Interval Notation

[1, \infty)

Solution steps

Vertex of

2 x^{2} + 4 x + 3 :

Minimum

(- 1, 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}) = (- 1, 1)

f (x) \geq 1

Popular Examples

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lo g_{3} (x - 1) + 3

amplitude of-1/5 cos(1/5 x)amplitude

- \frac{1}{5} cos (\frac{1}{5} x)

critical |sin(4x)+5cos(4x)|critical points

∣ sin (4 x) + 5 cos (4 x) ∣

range of 1/(sqrt(e^x+1))range

\frac{1}{e ^{x} + 1}

Frequently Asked Questions (FAQ)

What is the range of f(x)=2x^2+4x+3 ?
The range of f(x)=2x^2+4x+3 is f(x)>= 1