Complete the table of values for the equation y = x2 − 2x − 4.

We will substitute each $x$ value into the equation to find the corresponding $y$ value. Note that the value for $x=0$ in your table is incorrect; it should be $-4$.

For $x = -2$:

For $x = -1$:

For $x = 0$:

For $x = 1$:

For $x = 2$:

For $x = 3$:

For $x = 4$:

The completed and corrected table of values is:

Plot the points from the table on a graph paper. The points are $(-2, 4)$, $(-1, -1)$, $(0, -4)$, $(1, -5)$, $(2, -4)$, $(3, -1)$, and $(4, 4)$. Connect these points with a smooth curve to form a parabola.

To solve $x^2 - 2x - 4 = 0$ graphically, find the points where the graph of $y = x^2 - 2x - 4$ intersects the x-axis (where $y=0$).
From the table, we observe:

• For $x$ between $-2$ and $-1$, $y$ changes from 4 to $-1$. This means the graph crosses the x-axis somewhere in this interval.
• For $x$ between 3 and 4, $y$ changes from $-1$ to 4. This means the graph crosses the x-axis somewhere in this interval.

By looking at the graph you draw, estimate the $x$-values where the curve crosses the x-axis.
The approximate solutions are: