PLEASEEE
The graph below shows a company's profit f(x), in dollars, depending on the price of pens x, in dollars, sold by the company:

Graph of quadratic function f of x having x intercepts at ordered pairs 0, 0 and 6, 0. The vertex is at 3, 120.

Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? (4 points)

Part B: What is an approximate average rate of change of the graph from x = 3 to x = 5, and what does this rate represent? (3 points)

Part C: Describe the constraints of the domain. (3 points)

A. x-intercepts are the breakeven prices, where there's no profit no loss. When the price is 0 or 6, there's no protit

Vertex is the max profit and it's correspondence price.

The max profit is 120 when the price is 3.

Increasing: 0 < x < 3

Profit increases as price increases

Decreasing: 3 < x < 6

Profit decreases as price increases

B. f(x) = a(x - 3)² + 120

Using (0,0)

0 = 9a + 120

a = -40/3

f(x) = (-40/3)(x - 3)² + 120

f(5) = 200/3

f(3) = 120

Rate of change:

(200/3 - 120) ÷ (5 - 3)

-80/3

In this interval, on average as the price goes up by $1, profit decreases by $80/3

C. 0《x《6

x < 0 is not possible because price can not be negative

x > 6 will give negative profit, so no production

i can you, i love poetry

area = length x width

length = 2 x width

32 = 2 x width x width

32 = 2 x width^2

36 = width ^2  

width = 6

length = 12

area is 32

perimeter = 2 x 12 + 2 x 6 = 24 + 12 = 36

step-by-step explanation: