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.

Visualize the 3D graph of the elliptic paraboloid defined by z = x^2 + 16y^2. Understand the effect of different coefficients on the x and y variables, and explore key concepts in multivariable calculus. Suitable for college-level students.

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