Question

in the following questions, look at different ways to represent the relation given by the equation $y = x^2 - 1$. the table shows some values for the given equation. find the values of $a$ and $b$. \

$$\begin{tabular}{|c|c|c|c|c|} \\hline $x$ & $-2$ & $-1$ & $b$ & $1$ \\\\ \\hline $y$ & $a$ & $0$ & $-1$ & $0$ \\\\ \\hline \\end{tabular}$$

$a = \square$ $b = \square$

Explanation:

Step1: Find the value of \( a \)

We know the equation is \( y = x^2 - 1 \). When \( x = -2 \), substitute \( x \) into the equation:
\( y = (-2)^2 - 1 \)
\( y = 4 - 1 = 3 \)
So \( a = 3 \).

Step2: Find the value of \( b \)

When \( x = b \), \( y = -1 \). Substitute into the equation \( y = x^2 - 1 \):
\( -1 = x^2 - 1 \)
Add 1 to both sides: \( x^2 = 0 \)
So \( x = 0 \), thus \( b = 0 \).

Answer:

\( a = 3 \), \( b = 0 \)