Super grocery carries a 128 ounce jug of iced tea. the nutrition label states that the jug serves 16 people. which rate best represents the relationship between the number of ounces of iced tea and the number of servings?

see below

Step-by-step explanation:

A.  f(x) = 4x^2 - 7x - 15

We need the numbers to multiply to- 15

1*15  and 3*5  

One of the terms multiplies by 4 (or 2)

Try 4 first

4*-3 +5 = -7   That works

-3+5 = -15

f(x) = (4x+5)(x-3)

B.  We want the x intercepts so set equal to 0

0 = (4x+5)(x-3)

Using  the zero product  property

0 = 4x+5    x-3 =0

-5 = 4x           x=3

-5/4 =x            x=3

C  End behavior

Let x be negative infinity

The function is dominate by 4x^2

f(-∞) = 4 ( -∞) ^2 = 4 (∞) = ∞  

At negative infinity the functions goes to infinity

Let x be  infinity

The function is dominate by 4x^2

f(∞) = 4 ( ∞) ^2 = 4 (∞) = ∞  

At  infinity the functions goes to infinity

Part D:

We know the zeros at 3 and -5/4

We know the vertex is at  halfway between the zeros

(3 -5/4) /2 =  7/4 /2 = 7/8

Since the parabola opens up (The coefficient of the x^2 term is positive), we know we have a minimum.

f(7/8) = 4 (7/8)^2 -7(7/8) -15 = 4(49/64) -1/8 -15 =-289/16

We know the minimum the zeros and the end behavior, we can graph the functions