Question

Jared is an intern at a real estate broker’s office. He was asked to record data on the difference of the number of sales made each month by the whole team of realtors and the average number of sales made by similar broker’s offices.
After gathering the current year’s data, Jared decided to include the previous year’s data as well. Using all of the data, he created this function
to model the team’s sales, where X is the number of months since January, when Jared began gathering data, and f(x) is the number of sales as compared with the average. (Shown in picture)

1.) Use the graph to interpret and match the approximate intervals with their descriptions. Drag the tiles to the correct boxes. Not all tiles will be used.

Tiles: (-6.3, 10), (-3, 10), (-9, 0), (4.9, 10), (0, 4.9), (-9, -3)

Pairs:
interval over which the difference of the numbers of the sales is increasing =

interval over which the difference of the numbers of sales is negative =

interval over which the difference of the numbers of sales is increasing =

interval over which the difference of the numbers of sales is positive =

2.) Use graph to complete the statements. Select the correct answer from the drop-down menu.

The team’s total number of sales is equal to the average number of sales at BLANK months from when Jared began gathering data

options: -6.3 and 5; -9, -3, and 10; 3, 9, and 10; -13.5

The team’s minimum number is sales this year occurred at approximately BLANK months from when Jared began gathering data.

options: 7; -6; 5; 0; -28

3.) What are the factors of the equation representing Jared’s function? Select all that apply.

(x-10)
(x-9)
(x+10)
(x+3)
(x+9)
(x-3)

4.) Use the factors of the function and the y-intercept to find the standard form of the equation representing Jared’s function. Type the correct answer in the box.

5.) Jared also gathered data from a competing real estate broker’s office. The competitor’s sales were equal to the average number of sales 8 months before Jared begun gathering data and again 2 and 6 months after he began gathering data. The relative minimum number of sales was lower than the relative minimum number of sales of Jared’s office.

Use the sliders for a, b, c, and d to create a graph that could model the competitor’s number of sales.

I mostly need help with PART B and PART E!! Please help me out

Answer 1

I think it’s gonna be c

Answer 2

Answer:

okay y'all I finally got it after 4 different tutors and 6 hours of work lol so here you go :).

Part A:

interval over which the difference of the numbers of sales is positive = (-9,-3)

interval over which the difference of the numbers of sales is negative = (-3,10)

interval over which the difference of the numbers of sales is increasing = (4.9,10)

interval over which the difference of the numbers of sales is decreasing = (0,4.9)

Part B:

-9, -3, 10

5

Part C:

(x + 9), (x + 3), and (x - 10)

Part D:

0.05x^3 + 0.1x^2 -4.65x - 13.5

pArT e:

goodness this one was a mess...

0.65(x+8)(x-2)(x-6) (make sure to put the opposite sign of the factors in the place where the sliders are because its in (x-m) form.      

Step-by-step explanation:

For all those people who want to know how to do the problem instead of just what the answer is, i gOcHu! im the same way and fr i went through 3 tutors who just told me what the answer is and didnt tell me how. So here are your explinations :).

Part A

This one was kind of self explanatory. The graph was increasing and decreasing at the obvious points and the graph was positive and negative at other certain points on the graph as shown in the answers.

Part B

The average number of sales is shown by the y axis, so knowing this, we can see that when we cross a point on the graph that has y = 0. In this case, the x values are -9, -3, and 10. So at these points, the number of sales is at the average.

Part C

One of the formulas in algebra states that is you have a factor of f(x) that is f(x) = (x-m) then m = an x-intercept. Knowing this we can conclude that every x-intercept we find on the given graph is a factor of the graph's equation if you substitute that x-intercept integer for m in (x-m). When we do this, we find that there are three factors of the graphs equation so far which are (x-10), (x+3), and (x+9).

Part D

We know that to find the standard form of the equation, we must first find 'a' in a(x-b)(x-c)(x-d). To do this we must set x as 0 and f(x) as the y-intercept to create the equation -13.5 = a(0+9)(0+3)(0-10). To solve this we would first solve what's inside the parenthesis, so now our equation has been simplified to -13.5 = a(9)(3)(-10). After this step, we then must multiply and then distribute in 'a'. This gives us -13.5 = -270a. Now to solve for a we must divide each side by -270 which then gives us our answer: a = 0.05. Now we can substitute 0.05 for 'a' so now our factored equation is 0.05(x+9)(x+3)(x-10). Now, in order to find the standard form of our equation we have to multiply and distribute and foil a whole bunch until we get our answer: 0.05x^3+0.1x^2-0.65x-13.5. We also know that the y-intercept in these kind of equations is always that last number containing no x but doing the multiplication to find it is still important. Goodness that was a lot haha.

Part E

oKaY. Soooooo, here is where I started having cRaZy iNsAnE problems. I got the factors by looking at the word problem and seeing that the competitor's sales matched the average sales at months -8, 2, and 6. Knowing that the x-axis represents the months and recalling the algebraic formula we used earlier, I know that the factors of this equation are (x+8), (x-2), and (x-6). So now we have the question of what is 'a'. I am still talking with a tutor abt that part im so sorry but ill update when i fully understand so i can help yall out. if you made it this far fr you are an amazing person and that kind of perseverance and work ethic is going to take you places :).

I hope some of this made sense, if not just go ahead and comment and ill try to clear things up. Im here for yall cuz no one was there for me. I hope that i could help :)).