How is the graph of y = -6x² + 4 different from the graph of y = -6x²

Solution:

Given, y = -6x² + 4 and y = -6x²

Consider y = -6x² + 4

⇒ (y - 4) = -6x²

⇒ x² = -(1/6)(y - 4)

Compare the above equation with (x - h)² = 4a(y - k) which is a parabola with its vertex at (h, k) = (0, 4) and the axis is along the y - axis and opens downwards.

Now consider y = -6x²

⇒ x² = -1/6 y

Compare the above equation with x² = 4ay which is a parabola with its vertex at origin (0, 0) and axis along the y-axis and opens downwards.

Thus, only a shift in vertex position can be observed which can be seen in the graph below.

How is the graph of y = -6x² + 4 different from the graph of y = -6x²

Summary:

The difference in the graph of y = -6x² + 4 and the graph of y = -6x² is a shift in the vertex position.