Final answer:
To check if an equation represents a graph, compare the graph of the equation with the given graph. Adjust constants or variable powers in the equation to make it fit better, or use regression methods for greater accuracy.
Step-by-step explanation:
To decide whether the equation y = (x + 3)(x + 1)(x − 2)^2 represents a given graph, you need to plot the graph of the equation and compare it to the given graph. If they match, it means the equation is a good representation of the graph. If they don't match, adjustments are needed.
You can make it a better fit for the graph by adjusting the constants or the powers of the variables. For example, if the graph shows a parabola opening upwards, but the equation produces a curve with extra wiggles or turns, you might need to simplify the equation to a quadratic form, such as y = ax^2 + bx + c, where a, b, and c are constants that define the shape and position of the parabola.
To find a better-fitting equation, you might also consider regression methods to fit the equation to data points from the graph, ensuring a more accurate representation of the data's trend.