The best-fit curve is represented by the equation y=0.4x^2 +1.2x+3. Hence the correct option is a.
The best-fit curve is determined by finding the quadratic equation that minimizes the sum of squared differences between the observed data points and the predicted values from the equation. In this case, the provided data points correspond to various values of x and their corresponding y values. The quadratic equation y=0.4x^2 +1.2x+3 is identified as the best-fit curve because it yields the least overall deviation from the actual data points when squared differences are summed.
This process, often done through statistical methods like least squares regression, ensures that the curve closely represents the observed trends in the given data set. The coefficients of the quadratic equation indicate the impact of each term on the curve, with 0.4 determining the curvature, 1.2 influencing the linear component, and 3 being the constant term. Hence the correct option is a.