What is the y=6x^2+36x+54 ?

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Find the Standard Form of the Parabola y=6x^2+36x+54

y = 6 x^{2} + 36 x + 54

Domain : - \infty < x < \infty

Range : f (x) \geq 0

X Intercepts : (- 3, 0), Y Intercepts : (0, 54)

Vertex : Minimum (- 3, 0)

Inverse : \frac{- 18 + 6 x}{6}, - \frac{6 x + 18}{6}

Interval Notation

Domain : (- \infty, \infty)

Range : [0, \infty)

Solution steps

Domain of

6 x^{2} + 36 x + 54 : - \infty < x < \infty

Range of

6 x^{2} + 36 x + 54 : f (x) \geq 0

Axis interception points of

6 x^{2} + 36 x + 54 :

X Intercepts

: (- 3, 0),

Y Intercepts

: (0, 54)

Vertex of

6 x^{2} + 36 x + 54 :

Minimum

(- 3, 0)

Inverse of

6 x^{2} + 36 x + 54 : \frac{- 18 + 6 x}{6}, - \frac{6 x + 18}{6}

4 x - 3 y = 18

f (x) = x^{2} - x + 5

y = arctan (x)

- 3 y = - 12

3 x - 4 y = - 8