Final answer:
The equation x² + 2z² = 1 represents an ellipse because it involves two squared terms with positive coefficients and sums to one. The correct graph matching this equation is Graph B: Ellipse.
Step-by-step explanation:
The student is asking to match the equation x² + 2z² = 1 with its corresponding graph. This equation represents a type of conic section. Conic sections include shapes like circles, ellipses, parabolas, and hyperbolas, which are obtained by intersecting a cone with a plane. This particular equation is that of an ellipse because it has two squared variables with different coefficients, which are positive, and the equation equals 1. In this case, x² has a coefficient of 1 and z² has a coefficient of 2, indicating that the ellipse is stretched more along the z-axis than the x-axis.
To match the given equation to the correct graph, we will look for the one that represents an ellipse. As such, the correct match for the equation x² + 2z² = 1 with the options provided would be Graph B: Ellipse.