Question 625792
For the given equation, list the intercepts and test for symmetry.
y = x^3 - 216
This equation is a difference of cubes
{{{y = x^3 - 6^3}}}
{{{a^3-b^3=(a-b)(a^2+ab+b^2)}}}
{{{y=(x-6)(x^2+6x+36)}}}
x-intercepts
set y=0
{{{0=(x-6)(x^2+6x+36)}}}
x=6
two other roots are non-real {{{(b^2-4ac)<0}}}
y-intercept
set x=0
y=-6*36=-216
symmetry:none
see graph below:
{{{ graph( 300, 300, -10, 10, -1000, 1000,x^3-6^3) }}}