6. Which of the following describes the parabola with the equation y = 4x^2 − 12x + 9?

A. The axis of symmetry is x = 4 and the vertex is (4, −12).

B. The axis of symmetry is x = −1.5 and the vertex is (−1.5, 36).

C. The axis of symmetry is x = 0 and the vertex is (0, 9).

D. The axis of symmetry is x = 1.5 and the vertex is (1.5, 0).

D. The axis of symmetry is x = 1.5 and the vertex is (1.5, 0).

Step-by-step explanation:

y=4x^2-12x+9:\quad \mathrm{Parabola\:with\:vertex\:at}\:\left(h,\:k\right)=\left(\frac{3}{2},\:0\right),\:\mathrm{and\:focal\:length}\:|p|=\frac{1}{16}

To find the vertex of this parabola, "complete the square:"  Rewrite y = 4x2 - 12x + 9 in the form y = 4(x - h)^2 + k:

y = 4x^2 - 12x + 9  =>  y = 4(x^2 - 3x) + 9.

Now complete the square of x^2 - 3x:  Take half of -3 and square the result, obtaining (-3/2)^2, or 9/4.  Add 9/4 to x^2 - 3x and then subtract 9/4 from the result:  We get x^2 - 3x + 9/4 - 9/4.  Substitute this result back into

y = 4(x^2 - 3x) + 9:  y = 4(x^2 - 3x + 9/4 - 9/4) + 9

and then rewrite the perfect square x^2 - 3 + 9/4 as the square of a binomial:

                                y = 4(x - 3/2)^2 - 9/4) + 9.  This simplifies to:

                                y = 4(x - 3/2)^2 + 0.

Thus, the vertex is at            (3/2, 0) and the axis of symmetry is x = 3/2.  This agrees with Answer B.

Given : equation y = 4x^2 − 12x + 9

To Find  :

A) The axis of symmetry is x = 0 and the vertex is (0,9).

B)The axis of symmetry is x= 1.5 and the vertex is (1.5, 0).

C)The axis of symmetry is x = 4 and the vertex is (4, -12).

D)The axis of symmetry is x = -1.5 and the vertex is (-1.5, 36).

Solution:

y =  4x² - 12x  + 9

=> y = (2x)² - 2(2x)3  + 3²

=> y = (2x - 3)²

=> y = 4(x - 3/2)²

=> y = 4(x - 1.5)²

Axis of symmetry is x= 1.5  

Vertex  = (1.5 , 0)

The axis of symmetry is x= 1.5 and the vertex is (1.5, 0).

(B)17

Step-by-step explanation:

The dump truck is 21 feet long, 8 feet wide, and 6 feet tall.

Volume of the dump truck=21 X 8 X 6=1008 cubic feet

Since the dump bin can hold dirt equivalent to 1.2 times its capacity,

Volume of dirt the truck can hold=1.2 X 1008=1209.6 cubic feet

If the truck wants to haul 20,000 cubic feet of dirt.

Minimum number of trips=20000/1209.6=16.53 Trips

We round this up to 17 since there is no half trip.

Therefore, the minimum number of trips needed to haul 20,000 cubic feet of dirt is 17.