Each equation given below describes a parabola. Which statement best compares their graphs?x = 2y2               x = 8y2

1. Break Down the Problem

We need to compare the two given equations of parabolas:

• Equation 1: $x = 2y^2$
• Equation 2: $x = 8y^2$

2. Relevant Concepts

The standard form of a parabola that opens to the right is given by $x = ky^2$, where $k$ is a constant that affects the width and orientation of the parabola:

• A larger value of $k$ results in a narrower parabola.
• A smaller value of $k$ leads to a wider parabola.

3. Analysis and Detail

For our equations:

• Equation 1: $k = 2$
• Equation 2: $k = 8$

Since $8 > 2$, the second parabola (Equation 2) opens more narrowly compared to the first parabola (Equation 1).

4. Verify and Summarize

We can summarize that the parabolas open in the same direction (to the right), but the width of the parabolas is different. The parabola represented by $x = 8y^2$ is narrower than the one represented by $x = 2y^2$.

Final Answer

The statement that best compares their graphs is: The parabola $x = 8y^2$ is narrower than the parabola $x = 2y^2$.