Final answer:
The equation for the new graph is y = -3(x - 4)².
Step-by-step explanation:
To find the equation for the new graph, we need to go through the given transformations step by step. First, the graph is dilated by a factor of 3 from the x-axis, which means the x-values are multiplied by 3. This gives us y = (3x)². Next, the graph is reflected in the x-axis, which means the y-values are multiplied by -1. This gives us y = -(3x)². Finally, the graph is translated 4 units in the negative direction of the x-axis, which means we subtract 4 from the x-values. This gives us y = -(3(x - 4))². Therefore, the correct equation for the new graph is (B) y = -3(x - 4)².
Dilation by a factor of 3 from the x-axis: This means we will multiply the 'y' value by 3, which changes our equation to y = 3x².
Reflection in the x-axis: A reflection in the x-axis changes the sign of the 'y' value, making the new equation y = -3x².
Translation 4 units in the negative direction of the x-axis: This involves subtracting 4 from 'x' before squaring it, yielding the final equation y = -3(x + 4)².
Putting this all together, the final answer is B. y = -3(x - 4)².