Question 1077218

What's the equation of the parabola {{{y=ax^2+bx+c}}} which passes through the points of ({{{0}}}, {{{3}}}), ({{{1}}},{{{4}}}), and ({{{2}}},{{{ 3}}})? 

use given points to find {{{a}}},{{{b}}},and {{{c}}}

 {{{y=ax^2+bx+c}}}...............for point ({{{0}}}, {{{3}}})

{{{3=a*0^2+b*0+c}}}
{{{3=c}}}.........eq.1

 {{{y=ax^2+bx+c}}}............for {{{3=c}}} and  ({{{1}}},{{{4}}})

 {{{4=a*1^2+b*1+3}}}
{{{4=a+b+3}}}
{{{1=a+b}}}.........solve for {{{a}}}
{{{a=1-b}}}..........eq.2

 {{{y=ax^2+bx+c}}}............{{{3=c}}},{{{a=1-b}}}, and ({{{2}}}, {{{3}}})
 {{{3=(1-b)2^2+b*2+3}}}
{{{3-3=(1-b)4+2b}}}
{{{0=4-4b+2b}}}
{{{0=4-2b}}}
{{{2b=4}}}
{{{b=2}}}........eq.3

find {{{a}}}
{{{a=1-b}}}..........eq.2
{{{a=1-2}}}
{{{a=-1}}}

so, your equation is:

{{{y=-x^2+2x+3}}}

and your answer is: D.) {{{y=-x^2+2x+3}}}