Question 993481
{{{y=( x+3 ) ( x^2+3x-3 )}}}

intersection with the x-axis occurs where {{{y=0}}}
and 
intersection with the y-axis occurs where {{{x=0}}}

so set {{{y=0}}} and find intersection with the x-axis

{{{0=( x+3 ) ( x^2+3x-3 )}}}...will be true for {{{( x+3 )=0}}} or {{{( x^2+3x-3 )=0}}}, or both 

if {{{( x+3 )=0}}}=>{{{highlight(x=-3)}}}

 {{{( x^2+3x-3 )=0}}}...use quadratic formula

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 

{{{x = (-3 +- sqrt( 3^2-4*1*(-3) ))/(2*1) }}} 

{{{x = (-3 +- sqrt( 9+12 ))/2 }}}

{{{x = (-3 +- sqrt( 21 ))/2 }}}

solutions: exact solutions

{{{highlight(x = (-3 + sqrt( 21 ))/2 )}}}

or

{{{highlight(x = (-3 - sqrt( 21 ))/2) }}}

approximate solutions:

{{{x = (-3 + sqrt( 21 ))/2 }}}

{{{x = (-3 + 4.6)/2 }}}

{{{x = (1.6)/2 }}}

{{{highlight(x =0.8 )}}}

or

{{{x = (-3 - sqrt( 21 ))/2 }}}

{{{x = (-3 - 4.6)/2 }}}

{{{x = (-7.6)/2 }}}

{{{highlight(x =-3.8) }}}


so, ordered pairs are:
({{{-3 }}},{{{0}}})
({{{(-3 + sqrt( 21 ))/2 }}},{{{0}}})
({{{(-3 - sqrt( 21 ))/2 }}},{{{0}}})

or
({{{-3 }}},{{{0}}})
({{{0.8 }}},{{{0}}})
({{{-3.8 }}},{{{0}}})


now find y-intercept:
 
the y-axis occurs where {{{x=0}}}, so set {{{x=0}}}

{{{y=( 0+3 ) ( 0^2+3*0-3 )}}}

{{{y=( 3 ) ( -3 )}}}

{{{highlight(y= -9)}}}

ordered pair is:

({{{0 }}},{{{-9}}})


see it on the graph:

{{{ graph( 600, 600, -15, 15, -15, 15,( x+3 ) ( x^2+3x-3 )) }}}