Question

Draw the graphs of
$y=x^2-x-6$
and find the zeroes in each case.

Answer 1

$y=x^2-x-6$
When $x=-3$
$y=-3^2-(-3)-6=9+3-6=6$
When $x=-2$
$y=-2^2-(-2)-6=4-2-6=0$
When $x=-1$
$y=-1^2-(-1)-6=1+1-6=-4$
When $x=0$
$y=0^2-0-6=6$
When $x=1$
$y=1^2-1-6=-6$
When $x=2$
$y=2^2-2-6=4-8=-4$
When $x=3$
$y=3^2-3-6=9-9=0$

List of $x$ and $y$
$x-3-2-10123$
$y60-4-6-6-40$

$(x,y)=(-3,6),(-2,0),\left(\right(-1,-4),(0,-6),(1,-6),(2,-4).(3,0)$

$\therefore$The graph $y=x^2-x-6$cuts $X-$axis at the points $3$ and $-2$
$\therefore$ The zeroes of quadratic polynomial are $-2$ and $3.$