Final answer:
The cost function c(x) = 150 + 2,900x - 0.02x² is a quadratic equation since it includes an x² term, fitting the standard quadratic form ax² + bx + c.
Step-by-step explanation:
The given cost function c(x) = 150 + 2,900x - 0.02x² represents the cost, in thousands of dollars, of airing x television commercials during a sports event. The function is a second-degree polynomial because of the x² term, making it a quadratic equation. The standard form of a quadratic equation is ax² + bx + c, and the given function fits this form with coefficients a = -0.02 (the coefficient of x²), b = 2,900 (the coefficient of x), and c = 150 (the constant term).
The given expression, c(x) = 150 + 2,900x - 0.02x², represents a quadratic function because it has a term with the variable x squared. A quadratic function is a second-degree polynomial function that can be written in the form y = ax² + bx + c, where a, b, and c are constants and a ≠ 0. In this case, a = -0.02, b = 2900, and c = 150, which are all constants. Therefore, the given expression is a quadratic equation.