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A company makes and sells sports bicycles. After analyzing demand for the bicycles, they determine that if they set the price of the bicycles to $120 or $350, they will break even (earn zero profit). Which function below could model this?

Respuesta :

Using quadratic function concepts, the function that could model this is:

[tex]f(x) = -x^2 + 470x - 42000[/tex]

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  • If the price is too small, the profit is negative.
  • The same is true if the price is too high.
  • If the price is in the desired range, the profit is positive.
  • The break-even point is when the profit is 0.
  • The break-even points are $120 and $350, thus, they are the zeros of a quadratic equation.
  • The function is positive between the zeros, thus the leading coefficient is negative.
  • The function can be given by:

[tex]f(x) = a(x - x_1)(x - 2)[/tex]

  • In which [tex]x_1[/tex] and [tex]x_2[/tex] are the zeros, thus:

[tex]f(x) = -1(x - 120)(x - 350)[/tex]

[tex]f(x) = -x^2 + 470x - 42000[/tex]

A similar problem is given at https://brainly.com/question/23991455

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