Question

1. which graph corresponds to the equation $x^2 - y^2 = 16$?

Explanation:

Step1: Rewrite to standard hyperbola form

Divide both sides by 16:
$$\frac{x^2}{16} - \frac{y^2}{16} = 1$$

Step2: Identify conic section type

The equation matches the standard form of a horizontal transverse axis hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, with $a=4$, $b=4$. This graph opens left and right.

Step3: Match to given graphs

The first graph shows a hyperbola opening left/right, consistent with the equation. The second is an ellipse, third is a parabola, which do not match.

Answer:

The first graph (the hyperbola opening left and right with vertices at $(\pm 4, 0)$, scaled to the grid shown)