The graph of y = 8x² + 1 is similar to the graph of y = 8x² in that both represent parabolic shapes that open upwards due to the positive coefficient of x². However, there is a key difference between the two graphs regarding their position on the coordinate plane.
Specifically, the graph of y = 8x² has its vertex at the origin (0,0). In contrast, the graph of y = 8x² + 1 is shifted vertically upwards by 1 unit. This means that the vertex of the second graph is located at (0,1).
This vertical shift does not affect the shape or width of the parabola. Both graphs will still open upwards and have the same degree of steepness defined by the coefficient 8, but the entire graph of y = 8x² + 1 will appear higher on the y-axis compared to y = 8x².