What is the equation of the curve of best fit shown in the graph? A. \( y=\frac{1}{2} x^{2}+\frac{5}{2} x+3 \) B. \( y=\frac{1}{2} x^{2}+\frac{1}{2} x+3 \) C. \( y=-\frac{1}{2} x^{2}+\frac{1}{2} x+3 \) D. \( y=-\frac{1}{2} x^{2}+\frac{1}{2} x-3 \)

To find the equation of the curve of best fit that matches the shape of the graph, we can note that the highest degree term is quadratic, indicated by the presence of \(x^2\). Given that the curve likely opens downwards, we can rule out options that have a positive leading coefficient. Therefore, we will focus on the equations with a leading term of \(-\frac{1}{2} x^{2}\). Out of options C and D, we need to assess the y-intercept and the other coefficients to find the best match with the graph. As a little tip, check for common mistakes like overlooking the signs of coefficients and mistakenly assuming the curvature from the graph. Remember, sketching a rough shape can also help in visualizing which equation aligns best with the given data!