Question

q2. complete the table for $y = x^2 - 2x - 3$.
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$$\begin{tabular}{|c|c|c|c|c|c|c|c|} \\hline $x$ & $-2$ & $-1$ & $0$ & $1$ & $2$ & $3$ & $4$ \\\\ \\hline $y$ & $5$ & $0$ & $-3$ & $-4$ & $-3$ & & \\\\ \\hline \\end{tabular}$$

draw the graph of $y = x^2 - 2x - 3$. label the graph as $y = x^2 - 2x - 3$.

Explanation:

Step1: Calculate y when x=3

Substitute $x=3$ into $y=x^2-2x-3$
$y=(3)^2 - 2(3) - 3 = 9 - 6 - 3 = 0$

Step2: Calculate y when x=4

Substitute $x=4$ into $y=x^2-2x-3$
$y=(4)^2 - 2(4) - 3 = 16 - 8 - 3 = 5$

Step3: List plotted points

The complete set of $(x,y)$ points is:
$(-2,5), (-1,0), (0,-3), (1,-4), (2,-3), (3,0), (4,5)$

Step4: Describe graph plotting

Plot each point on the grid, then draw a smooth, symmetric parabola through all points, and label it $y=x^2-2x-3$.

Answer:

Completed table values:
When $x=3$, $y=0$; when $x=4$, $y=5$

The graph is a parabola passing through the points $(-2,5), (-1,0), (0,-3), (1,-4), (2,-3), (3,0), (4,5)$, labeled as $y=x^2-2x-3$.