Question 1179669


 Graph {{{y = x^2 + 5x + 6}}}


{{{ graph( 600, 600, -50, 50, -10, 50, x^2 + 5x + 6) }}}


 Determine the table of values and calculate the first and second differences.

{{{x}}}|{{{y}}}
{{{0}}}|{{{6}}}....{{{y = 0^2 + 5*0 + 6=6}}}
{{{1}}}|{{{12}}}....{{{y = 1^2 + 5*1 + 6=12}}}
{{{2}}}|{{{20}}}....{{{y = (2)^2 + 5*(2) + 6=20}}}
{{{3}}}|{{{30}}}....{{{y = (3)^2 + 5*(3) + 6=30}}}
{{{4}}}|{{{42}}}....{{{y = (4)^2 + 5*(4) + 6=42}}}


->the first difference 
{{{12-6=6}}}
{{{20-12=8}}}
{{{30-20=10}}}
{{{42-30=12}}}

the first differences are not same, means function is not linear

->the second difference 

{{{8-6=2}}}
{{{10-8=2}}}
{{{12-10=2}}}

the second differences are is {{{2}}}, means  we have quadratic model