Question 1131533
 Write an equation to represent the data shown in the table below. 
{{{x}}} | {{{y}}}
{{{-2}}} | {{{152}}}
{{{-1}}} |{{{76}}}
{{{0}}} | {{{38}}}


{{{y=ax^2-bx+c}}}

since given ({{{0}}} , {{{38}}})=>{{{c=38}}}

{{{y=ax^2-bx+38}}}..........use point {{{-1}}} , {{{76}}}

{{{76=a(-1)^2-b(-1)+38}}}

{{{76-38=a+b}}}

{{{a+b=38}}}

 {{{b=38-a}}}........(1)


{{{y=ax^2-bx+38}}}..........use {{{-2}}} , {{{152}}}

{{{152=a(-2)^2-b(-2)+38}}}

{{{152-38=4a+2b}}}

{{{114=4a+2b}}}

{{{57=2a+b}}}

{{{b=57-2a}}}.......(2)


from  (1) and (2) we have
 
{{{38-a=57-2a}}}

{{{2a-a=57-38}}}

{{{a=19}}}

then

{{{b=38-19}}}........(1)

{{{b=19}}}



and your equation is:

{{{y=19x^2-19x+38}}}


{{{drawing ( 600, 600, -10, 10, -165, 165,

circle(-2,152,.1),circle(0,38,.1),circle(-1,76,.1),
locate(-2,152,p(-2,152)),locate(-1,76,p(-1,76)),locate(0,38,p(0,38)),
graph( 600, 600, -10, 10, -165, 165, 19x^2-19x+38)) }}}