`y = x^2-5x-6`

`y = x^2-6x+x-6`

`y = x(x-6)+1(x-6)`

`y=(x-6)(x+1)`

x-intercept is given when y=0.

So, x-intercepts are (6,0) and (-1,0)

y-intercept is given when x=0

So y-intercept is at (0, -6).

Test of symmetry

A function is symmetric with respect to the x-axis if f(x)=-f(x).

(x-6)(x+1) is not equal to -(x-6)(x+1).

So, it is not symmetrical about x-axis.

A function is symmetric with respect to the y-axis if f(x)=f(-x).

(x-6)(x+1) is not equal to (-x-6)(-x+1).

So, it is not symmetrical about y-axis.

A function is symmetric with respect to the origin if f(x)=-f(-x).

(x-6)(x+1) is not equal to –((-x-6)(-x+1)).

So, it is not symmetrical about origin.