Question

Solve the equation $x^2-2x-3=0$ graphically.

Answer 1

Let us draw the graph of $y=x^2-2x-3$.
Now, form the following table by assigning integer values from $-3$ to $4$ for $x$ and finding the corresponding values of $y=x^2-2x-3$.

$x$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$	$4$
$x^2$	$9$	$4$	$1$	$0$	$1$	$4$	$9$	$16$
$-2x$	$6$	$4$	$2$	$0$	$-2$	$-4$	$-6$	$-8$
$-3$	$-3$	$-3$	$-3$	$-3$	$-3$	$-3$	$-3$	$-3$
$y$	$12$	$5$	$0$	$-3$	$-4$	$-3$	$0$	$5$

Plot the points $(-3,12),(-2,5),(-1,0),(0,-3),(1,-4),(2,-3),(3,0),(4,5)$ and join the points by a smooth curve.
The curve intersects the x-axis at the points $(-1,0)$ and $(3,0)$
The x-coordinates of the above points are $-1$ and $3$
Hence, the solution set is $\{-1,3\}$.
Note
(i) On the x-axis, $y=0$ always.
(ii) The values of $y$ are both positive and negative. Thus, the curve lies below and above the x-axis.
(iii) The curve is symmetric about the line $x=1$. (It is not symmetric about the y-axis)