Here is the 3D graph of the surface represented by the equation $z = x^2 + 16y^2$. You can see the paraboloid shape, with the stretching along the $y$-axis due to the factor of 16, making the surface flatter in that direction compared to the $x$-axis.

Would you like more details on this graph or any related concepts?

Here are 5 related questions to deepen your understanding:

1. How would the graph change if the equation was $z = 16x^2 + y^2$?
2. What is the effect of negative coefficients on the shape of the paraboloid?
3. How do you derive the equation of an elliptic paraboloid?
4. Can you find the cross-sections of the graph for specific values of $z$?
5. How does this equation change if you add a linear term, like $z = x^2 + 16y^2 + 3x + 4y$?

Tip: To better visualize surfaces like this, try examining cross-sections for fixed values of $x$ or $y$ to understand how the surface behaves in different slices.