20 POINTS PLZ HELP
A company produces remote-controlled helicopters. The company’s profit, in thousands of dollars, as a function of the number of helicopters produced per week can be modeled by a quadratic function. When 1 helicopter is produced per week, the company’s profit is 4 thousand dollars. The maximum profit, 22 thousand dollars, occurs when 4 helicopters are produced per week. If h is the number of helicopters produced per week, which function models the scenario?
f(h) = –4(h – 1)^2 + 4
f(h) = –2(h – 4)^2 + 22
f(h) = (h – 4)^2 + 22
f(h) = (h – 1)^2 + 4

In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function with one or more variables in which the highest-degree term is of the second degree.

What is Profit?

A financial gain, especially the difference between the amount earned and the amount spent in buying, operating, or producing something.

Given,

When 1 helicopter is produced per week, the company’s profit is $4000

When 4 helicopter is produced per week, the company’s profit is $22000

Consider the equation 2

f(h) is the function of company's profit in thousands of dollar

h is the number of helicopter produced per week

Then,

[tex]f(1) = -2(1-4)^{2}+22=4[/tex]

[tex]f(4) = -2(4-4)^{2}+22=22[/tex]

Both in thousands of dollars

Therefore,

When 1 helicopter is produced per week, the company’s profit is $4000

When 4 helicopter is produced per week, the company’s profit is $22000

Both the cases are satisfied

Therefore the function model is option(2) [tex]f(h) = -2(h-4)^{2}+22[/tex] other function model wont satisfy the above condition

Hence, If h is the number of helicopters produced per week, then the function model scenario is option(2) [tex]f(h) = -2(h-4)^{2}+22[/tex]

Learn more about Quadratic function and Profit here

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