Question 1187578

Axis vertical and passing through (0,0) , (1,0) and (5,-20)

 the equation of the parabola is:

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

Since the parabola passes through the point ({{{0}}},{{{0}}}), then {{{0=c}}}

so we have
{{{y=ax^2+bx }}}

Since the parabola passes through the point ({{{1}}},{{{0}}}), then 

{{{0=a*1^2+b*1 }}}

{{{0=a+b}}}......solve for {{{a}}}

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

Since the parabola passes through the point ({{{5}}},-20), then 

{{{-20=25a+5b}}}   ........substitute {{{a}}} from eq.1

{{{-20=25(-b)+5b}}}  
{{{-20=-25b+5b}}}  
{{{-20=-20b}}} 
{{{b=1}}}

go to
{{{a=-b}}}........eq.1...substitute {{{b}}}
{{{a=-1}}}

your equation is:

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


{{{ drawing( 600, 600, -10, 10, -25, 10,
circle(1,0,.12), locate(1,0.8,p(1,0)),
circle(5,-20,.12), locate(5,-20,p(5,-20)),
graph( 600, 600, -10, 10, -25, 10, -x^2+x )) }}}