Question

match each graph with its equation.

\\ \frac{x^2}{6^2} + \frac{y}{2} = 1 \\
\\ \frac{x^2}{6^2} + \frac{y^2}{2^2} = 1 \\
\\ -\frac{x}{6} + \frac{y^2}{2^2} = 1 \\
\\ -\frac{x^2}{6^2} + \frac{y^2}{2^2} = 1 \\

Explanation:

Step1: Identify key features of graph a

The graph is a horizontal parabola opening to the right with vertex at \((-6, 0)\) and \(y\)-intercepts at \((0, 2)\) and \((0, -2)\).

Step2: Test the points in the equations

Substitute \((-6, 0)\) and \((0, 2)\) into the third equation:

$$-\frac{-6}{6} + \frac{0^2}{2^2} = 1 + 0 = 1$$

$$-\frac{0}{6} + \frac{2^2}{2^2} = 0 + 1 = 1$$

Answer:

Graph a matches with the equation \(-\frac{x}{6} + \frac{y^2}{2^2} = 1\).