Question

A company produces and sells solar panels for $520. The company’s daily profit, P(x), can be modeled by the function P(x) = -6x squared + 156x +1,000, where x is the number of $5 price increases for each solar panel. Use the graph to answer the questions. Part A: Identify the approximate value of the y-intercept. Explain what the y-intercept means in terms of the problem scenario. Part B: Identify the appropriate value of the x-intercept. Explain what the x-intercept means in terms of the problem scenario. 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.

Answer 1

Part A : the y-intercept is approximately $1,000.

This represents the daily profit when there are no price increases.

Part B: the x-intercept is approximately 31.1

It represents the number of $5 price increases for each solar panel that make the profit zero.

Part C: the maximum of the function is 2000

This represents the maximum profit the company can make.

How x and y intercepts of a function is calculated.

Given

P(x) = -6x² + 156x + 1,000 = 0

PartA

The y-intercept is the value of the function when (x) is zero.

when (x = 0),

P(0) = -6(0)² + 156(0) + 1,000 = 1,000

So, the y-intercept is approximately $1,000.

In terms of the problem, this represents the daily profit when there are no price increases.

This means that the company sells solar panels at the base price of $520 each.

PartB

The x-intercept is approximately 31.1 from the graph

x = 31.10

It represents the number of $5 price increases for each solar panel that make the profit zero.

PartC

The maximum of the function occur where x = 13

from the graph.

x = -b/2a

= 156/-2*-6 = 13

At this value of x, y = 2000

This represents the maximum profit the company can make.