Question 132740
The equation, as you presented it, doesn't have any "intercepts."  This quadratic equation has two solutions or roots that would be the x-intercepts of the function {{{y = f(x) =x^2 + 8x +12}}}.  This function would also have a y-intercept at (0,f(0)).


If you meant to ask for the x-intercepts of {{{y = f(x) =x^2 + 8x +12}}}, then the method to find them consists of setting the function equal to 0, resulting in the equation you provided, and then solving for x.


{{{x^2 + 8x +12 = 0}}}


6 * 2 = 12 and 6 + 2 = 8, so:


{{{(x+6)(x+2)=0}}}, therefore x = -6 or x = -2, and the x-intercepts of {{{y = f(x) =x^2 + 8x +12}}} are the two points denoted by the ordered pairs (-6,0) and (-2,0).


As previously discussed the y-intercept of {{{y = f(x) =x^2 + 8x +12}}} is at the point (0,f(0)).  {{{f(0) =0^2 + 8(0) +12=12}}}, so the y-intercept is at the point (0,12).