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Popular >

y=3x^2+12x+1

Solution

y = 3 x^{2} + 12 x + 1

Solution

Domain : - \infty < x < \infty

Range : f (x) \geq - 11

X Intercepts : (\frac{- 6 + 33}{3}, 0), (- \frac{6 + 33}{3}, 0), Y Intercepts : (0, 1)

Vertex : Minimum (- 2, - 11)

Inverse : \frac{- 12 + 12 x + 132}{6}, \frac{- 12 - 12 x + 132}{6}

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 11, \infty)

Solution steps

Domain of

3 x^{2} + 12 x + 1 : - \infty < x < \infty

Range of

3 x^{2} + 12 x + 1 : f (x) \geq - 11

Axis interception points of

3 x^{2} + 12 x + 1 :

X Intercepts

: (\frac{- 6 + 33}{3}, 0), (- \frac{6 + 33}{3}, 0),

Y Intercepts

: (0, 1)

Vertex of

3 x^{2} + 12 x + 1 :

Minimum

(- 2, - 11)

Inverse of

3 x^{2} + 12 x + 1 : \frac{- 12 + 12 x + 132}{6}, \frac{- 12 - 12 x + 132}{6}

Popular Examples

f(x)=arctan(sin(2x))

f (x) = arctan (sin (2 x))

f(x)=10x^2+60x+99

f (x) = 10 x^{2} + 60 x + 99

f(x)=(|x|)/(|x|+1)

f (x) = \frac{∣ x ∣}{∣ x ∣ + 1}

f(x)=3x^2-18x+4

f (x) = 3 x^{2} - 18 x + 4

f(x)=(2x)/(ln(2x))

f (x) = \frac{2 x}{ln ( 2 x )}

Frequently Asked Questions (FAQ)

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