A company produces and sells solar panels for $520. The company's daily profit, P(x), can be modeled by the function P(x) = −6x2 + 120x + 1,000, where x is the number of $5 price increases for each solar panel. Use the graph to answer the questions.

Graph of function p of x equals negative 6 x squared plus 120 x plus 1,000. The graph has the x-axis labeled as number of price increases, and the y-axis labeled as profit. The curve begins at (0, 1000), increases to the vertex at about (10, 1600), and decreases through about (26, 0).

Part A: Identify the approximate value of the y-intercept. Explain what the y-intercept means in terms of the problem scenario. (3 points)

Part B: Identify the approximate value of the x-intercept. Explain what the x-intercept means in terms of the problem scenario. (3 points)

Part C: Identify the approximate value of the maximum of the function. Explain what the maximum of the function means in terms of the problem scenario. (4 points)

PLEASE HELP WILL MARK BRAINLIEST

Respuesta :

Answer:

  A. $1000, the daily profit with no price increases

  B. about 26; the number of $5 price increases that reduces profit to 0

  C. $1600, the daily profit with a price increase of $50

Step-by-step explanation:

Given a graph of daily profit versus $5 price increases with points (0, 1000), (10, 1600), and (≈26, 0) identified, you want the meaning of the intercepts and the maximum.

Part A:

The problem statement tells you the y-intercept is (0, 1000), and that it represents the daily profit if no price increases are made.

Part B:

The approximate value of the x-intercept is given in the problem statement as (26, 0). The x-intercept means the profit will be near 0 if there are 26 increases of $5 in the price of the solar panels (to $650).

Part C:

The approximate value of the maximum is given in the problem statement as 1600 when x = 10. The maximum of the function means profit can be maximized at $1600 per day by raising the price of a solar panel by $5×10 = $50.

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