Find the vertex for the parabola given by the function ƒ(x) = −3x^2 − 6x.
a) (1, 3)
b) (−1, 3)
c) (−1/2, 2)
d) (−1/2, 3)

B) (−1, 3)  

Step-by-step explanation:

The standard form of a quadratic function is  

y = ax² + bx + c

The vertex form of a parabola is

y = a(x - h)² + k

where (h, k) is the vertex of the parabola.

h = -b/(2a) and k = f(h)

In your equation, ƒ(x) = −3x² − 6x

a = -3; b = -6; c = 0

Calculate h

h = -(-6)/2(-3)]

h = 6/(-6)

h = -1

Calculate k

k = -3(-1)² -6(-1)

k = -3 + 6

k = 3

So, h = -1, k = 3, a = -3

The vertex form of the equation is  f(x) = -3(x + 1)² + 3.

The vertex is at (-1, 3).

The figure below shows the graph of ƒ(x) = −3x² − 6x  with the vertex

at (-1, 3).

the probability is 0

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you