To determine which equation best models the sales data given by the company over a nine-month period, we need to identify the relationship between the months [tex]\( x \)[/tex] and the units sold [tex]\( y \)[/tex]. This relationship can be modeled using a polynomial function, specifically a quadratic equation based on the choices provided.
We have the following data:
- Months [tex]\( x \)[/tex]: 1, 2, 3, 4, 5, 6, 7, 8, 9
- Units sold [tex]\( y \)[/tex]: 800, 500, 400, 300, 200, 300, 450, 600, 800
Let's derive the best fit quadratic equation [tex]\( y = ax^2 + bx + c \)[/tex].
Upon analysis, the coefficients [tex]\( a, b, \)[/tex] and [tex]\( c \)[/tex] for the best fit quadratic equation can be determined as follows:
- Coefficient [tex]\( a \approx 34 \)[/tex]
- Coefficient [tex]\( b \approx -334 \)[/tex]
- Constant term [tex]\( c \approx 1,075 \)[/tex]
These coefficients most closely match the equation [tex]\( y = 34x^2 - 334x + 1,075 \)[/tex].
Therefore, the best equation to model the given data is:
A. [tex]\( y = 34x^2 - 334x + 1,075 \)[/tex]
