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

(3x-8) or (3x+8)

step-by-step explanation:

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: