Question 1206103


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

given:
({{{-1}}},{{{0}}}),({{{2}}},{{{-54}}}),({{{5}}},{{{-252}}})


use ({{{-1}}},{{{0}}})

{{{0=a(-1)^2+b(-1)+c}}}
{{{a-b+c=0}}}.......eq.1


use ({{{2}}},{{{-54}}})

{{{-54=a(2)^2+b(2)+c}}}
{{{-54=4a+2b+c}}}
{{{4a+2b+c=-54}}}.......eq.2


use ({{{5}}},{{{-252}}})

{{{-252=a(5)^2+b(5)+c}}}
{{{-252=25a+5b+c}}}
{{{25a+5b+c=-252}}}.......eq.3


solve the system:

{{{a-b+c=0}}}.......eq.1
{{{4a+2b+c=-54}}}.......eq.2
{{{25a+5b+c=-252}}}.......eq.3
_________________________

 subtract eq.1 from eq.2

{{{4a+2b+c-(a-b+c)=-54-0}}}
{{{4a+2b+c-a+b-c=-54}}}
{{{3a+3b=-54}}}
{{{a+b=-54/3}}}
{{{a+b=-18}}}
{{{a=-b-18}}}.....eq.1a


go to

{{{a-b+c=0}}}.......eq.1, substitute {{{a}}}
{{{-b-18-b+c=0}}}
{{{-2b+c=18}}}
{{{c=2b+18}}}....eq.2a


go to

{{{25a+5b+c=-252}}}.......eq.3, substitute {{{a}}} and {{{c}}}
{{{25(-b-18)+5b+2b+18=-252}}}
{{{25(-b-18)+5b+2b+18=-252}}}
{{{-18b - 432=-252}}}
{{{252-432=18b}}}
{{{-180=18b}}}
{{{b=-10}}}


go to

{{{a=-b-18}}}.....eq.1a, substitute {{{b}}}
{{{a=-(-10)-18}}}
{{{a=10-18}}}
{{{a=-8}}}

go to

{{{c=2b+18}}}....eq.2a, substitute {{{b}}}
{{{c=2(-10)+18}}}
{{{c=-20+18}}}
{{{c=-2}}}


your equation is:

{{{y=-8x^2-10x-2}}}