Question

Question was provided via image upload.

Explanation:

Split the equation into a system of equations

$$
LATEXBLOCK0
$$

Identify the graphical representations of the system

• \(y = x^2 - 1\) is a parabola with its vertex at \((0, -1)\) opening upwards.
• \(y = 3\) is a horizontal line passing through \(3\) on the \(y\)-axis.

Analyze the visible graph options

• The first visible graph shows a parabola with vertex at \((0, -1)\) and a line with a positive slope, which does not represent \(y = 3\).
• The correct graph must show the intersection of the parabola \(y = x^2 - 1\) and the horizontal line \(y = 3\).

Answer:

The graph that can be used to find the solution(s) to \(x^2 - 1 = 3\) is the one showing the intersection of the parabola \(y = x^2 - 1\) (with vertex at \((0, -1)\)) and the horizontal line \(y = 3\).

• (A) The graph showing the parabola \(y = x^2 - 1\) and a slanted line
• (B) The graph showing the parabola \(y = x^2 - 1\) and the horizontal line \(y = 3\) (Correct answer)