Question

for the equation $y = x^2 - 2$, (a) create a table with at least three ordered pairs that are solutions of the equation, and (b) graph the equation. (a) complete the following table of ordered pairs that are solutions of the equation. \

$$\begin{tabular}{|c|c|} \\hline x & y \\\\ \\hline -2 & \\square \\\\ \\hline 0 & \\square \\\\ \\hline 2 & \\square \\\\ \\hline \\end{tabular}$$

Explanation:

Step1: Substitute \( x = -2 \) into \( y = x^2 - 2 \)

\( y = (-2)^2 - 2 = 4 - 2 = 2 \)

Step2: Substitute \( x = 0 \) into \( y = x^2 - 2 \)

\( y = 0^2 - 2 = 0 - 2 = -2 \)

Step3: Substitute \( x = 2 \) into \( y = x^2 - 2 \)

\( y = 2^2 - 2 = 4 - 2 = 2 \)

Answer:

For \( x = -2 \), \( y = 2 \); for \( x = 0 \), \( y = -2 \); for \( x = 2 \), \( y = 2 \). So the completed table has \( y \)-values \( 2 \), \( -2 \), \( 2 \) corresponding to \( x = -2 \), \( x = 0 \), \( x = 2 \) respectively.