Question

Match the equation with its graph: y = 2x² + z²?

1) Graph A: y = x²
2) Graph B: y = 2x²
3) Graph C: y = 3x²
4) Graph D: y = 4x²

Answer 1

The equation y = 2x² + z² represents a quadratic function. To determine the matching graph, we compare the coefficients of the equation to the given options. The graph that matches the equation is Graph B: y = 2x².

Step-by-step explanation:

The equation y = 2x² + z² represents a quadratic function. In this equation, the coefficients of x² and z² determine the shape of the graph. When these coefficients are greater than 1, the graph will be narrower, and when they are less than 1, the graph will be wider. Therefore, comparing the equation y = 2x² + z² to the given options, we can conclude that:

1. Graph A: y = x² will be wider than y = 2x² + z²
2. Graph B: y = 2x² represents the same function as y = 2x² + z²
3. Graph C: y = 3x² will be narrower than y = 2x² + z²
4. Graph D: y = 4x² will be wider than y = 2x² + z²

Therefore, the matching equation with the given graph is Graph B: y = 2x².