Final answer:
The best fitting quadratic function can be determined by comparing the coefficients of the given functions to the data. The properties of the coefficients and the quadratic formula are used to examine the behavior and solutions of the functions.
"the correct option is approximately option C"
Step-by-step explanation:
To determine which quadratic function best fits the given data, we can compare the general form of a quadratic equation, which is ax² + bx + c = 0, to the provided options. We need to identify the quadratic function with coefficients that match patterns in the data set or known values that may be derived from the data.
Without specific data points to analyze here, we will look at the given quadratic functions and note their key characteristics. Functions with a > 0 open upwards, while those with a < 0 open downwards; the vertex of the function will be a minimum or maximum respectively. The term b affects the symmetry and the direction in which the graph shifts horizontally, while c is the y-intercept.
An important tool in solving quadratic equations is the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a), applicable to any quadratic equation in the form ax² + bx + c = 0. The quadratic formula provides the roots (solutions) of the quadratic equation, which can be compared against the given functions to see which one produces similar solutions.
To provide a definitive answer, we would need the specific data points. However, the student can use the general characteristics of the functions and the quadratic formula to calculate and compare the roots of the functions to the data points they have to find which function best fits their data.