Please help with a2-lvl c3 maths

sketch y=x^2 -x-6 and y=|x|^2 -|x|-6

please explain to me how would you sketch y=|x|^2 -|x|-6. I know this is y=f|(x)| which means it is a reflection in the y-axis. My knowledge is not great please help me.

Thanks.

The sketch for y= x^2 - x - 6 is basically a U shape. It goes through the x axis at -2 and 3 and goes through the y axis at -6.

The modulus graph is the same but you ignore what's on the left side of the y axis and reflect what is on the right in the y axis.

:) I hope this helps.

f(x) = x² - x - 6
let's factorize : -2 is an obvious root the other is +3 so

f(x) = (x+2)(x-3)
the graph of f is a parabola like a huge U
and the part between - 2 and 3 is under the horizontal x-axis.

as |x|^2 -|x|-6 = | f(x) |
the graph is the graph of f but the part under the horizontal is returned (multiplied by (-1))
so
x <= - 2 we have |f(x)| = f(x)
-2 <= x <= 3 we have |f(x)| = - f(x)
3 <= x we have |f(x)| = f(x)

hope it' ll help !!