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 e

Question

2 months ago

10

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 e

ach 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

Mathematics

2 answers:

Leona [12.6K] · Answer 1 · 2026-02-17T17:45:15+03:00

Leona [12.6K]2 months ago

5 0

I believe it’s option c

AnnZ [12.3K] · Answer 2 · 2026-02-17T17:47:10+03:00

Answer:

Alright everyone, I finally figured it out after consulting with 4 different tutors and spending 6 hours on it lol, so here it goes :).

Part A:

The interval during which the difference in sales is positive = (-9,-3)

The interval during which the difference in sales is negative = (-3,10)

The interval during which the difference in sales is increasing = (4.9,10)

The interval during which the difference in 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:

Wow, that one was a challenge...

0.65(x+8)(x-2)(x-6) (make sure to adjust the signs of the factors based on the sliders being in (x-m) format.

Step-by-step explanation:

For those interested in understanding how to solve the problem rather than just obtaining the answer, I get that! I struggled the same way and went through 3 tutors who simply provided answers without explanations. Therefore, I’m sharing my breakdown :).

Part A

This part was somewhat self-evident. The graph showed clear points of increase and decrease while the graph's values shifted between positive and negative at specific times as described in my answers.

Part B

The y-axis displays the average sales, so recognizing this helps us see where the graph intersects at y = 0, which occurs at x values of -9, -3, and 10. Here, the number of sales aligns with the average.

Part C

According to an algebra principle, if a factor of f(x) is expressed as f(x) = (x-m), then m represents an x-intercept. Thus, we can deduce that each x-intercept we identify on the graph corresponds to a factor of the equation of the graph when substituting the intercept for m in (x-m). This gives us three factors of the equation: (x-10), (x+3), and (x+9).

Part D

To find the equation in standard form, we first need to establish the coefficient 'a' in a(x-b)(x-c)(x-d). By substituting x = 0 for the equation's y-intercept, we arrive at -13.5 = a(0+9)(0+3)(0-10). Solving within the parentheses simplifies to -13.5 = a(9)(3)(-10). After simplifying, we find that -13.5 = -270a. To isolate 'a', we divide each side by -270, yielding a = 0.05. Thus, we can replace 'a' in our factored expression, resulting in 0.05(x+9)(x+3)(x-10). Following this, we proceed with multiplication and distribution to ultimately derive the standard form: 0.05x^3 + 0.1x^2 -0.65x - 13.5. While identifying the y-intercept is critical, it’s important to note that it’s consistently the last number without an x variable. Quite the workout, haha.

Part E

Alright, this is where I encountered significant challenges. I derived the factors by interpreting the word problem, recognizing that the competitor's sales corresponded to average sales at months -8, 2, and 6. Since the x-axis represents months and leveraging the algebra formula previously used, I can ascertain the factors of this equation as (x+8), (x-2), and (x-6). The question then arises regarding 'a'. I'm still discussing this aspect with a tutor, and I apologize for the uncertainty. I'll provide an update as soon as I have clarity, so I can assist others. If you’ve read this far, you're fantastic, and this determination is a valuable trait that will lead to success :).

I hope some of this explanation clarifies things; if not, feel free to comment, and I’ll attempt to clarify further. I’m here to help because I know the feeling of being unsupported. I truly hope I can be of assistance :)).