The given equation is expressed as
y = x^2 - x - 12
We would find the x and y intercepts. To find the x intercept, we would substitute y = 0 into the equation. We have
0 = x^2 - x - 12
We would factorise the equation. We would find two terms such that their sum or difference is - x and their product is - 12x^2. The terms are 3x and - 4x. By replacing - x with 3x - 4x, we have
x^2 + 3x - 4x - 12 = 0
By factorising, we have
x(x + 3) - 4(x + 3) = 0
Since x + 3 is common, then
(x + 3)(x - 4) = 0
x + 3 = 0 or x - 4 = 0
x = - 3 or x = 4
The x intercepts are x = - 3 and x = 4
To find the y intercept, we would substitute x = 0 into the equation. We have
y = 0^2 - 0 - 12
y = - 12
The y intercept is - 12
The next step is to test for symmetry with respect to the x axis. To do this, we would replace y with - y. We have
- y = x^2 - x - 12
Since - y = x^2 - x - 12 is not equal to y = x^2 - x - 12, it means that the equation is not symmetric with respect to the x axis.
The next step is to test for symmetry with respect to the y axis. To do this, we would replace x with - x. We have
y = (- x)^2 - -x - 12
y = x^2 + x + 12
Since y = x^2 + x + 12 is not the same as y = x^2 - x - 12, it means that the equation is not symmetric with repect to the y axis