Question

Draw the graph of $y=x^2-x-2$ and find its roots.

Answer 1

Method 1:
Prepare a table of value to $y=x^2-x-2$.

$x$ $-2$ $-1$ $0$ $1$ $2$

$y$ $4$ $0$ $-2$ $-2$ $0$

Draw the parabola. Write the coordinates of the intersecting point of the parabola with x-axis.
Note the co-ordinates of the intersecting points of the parabola with $x$-axis.
The coordinates where the parabola intersects the x-axis are the roots of the equation.
That coordinates are $B(-1,0)$ and $E(2,0)$.
$\therefore$ The roots are $x=-1$ and $x=2$

Method 2:

$x^2-x-2=0\Rightarrow x^2=x+2$
Consider $y=x^2$ and $y=x+2$

For $y=x^2$

$x$ $-2$ $-1$ $0$ $1$ $2$

$y$ $4$ $1$ $0$ $1$ $4$

For $y=x+2$

$x$ $0$ $1$ $-1$ $2$ $-2$

$y$ $2$ $3$ $1$ $4$ $0$

Draw the parabola and linear graph

Write the coordinates of the points where the straight line intersects with the parabola.
They are $B(-1,1)$ and $E(2,4)$.
$\therefore$ The roots are $x=-1$ and $x=2$.