Question 752526

{{{ x^2 - 2x - 24=y }}}

vertex form:

{{{ x^2 - 2x -24=y}}}.....complete square on left side



{{{ (x^2 -2x+__)-24 =y }}}

{{{ (x^2 -2x+1) -1-24=y +24}}}

{{{ (x -1)^2-25 =y }}}

vertex: {{{h=1}}} and {{{k=-25}}}

{{{x-intercepts}}}: set {{{y=0}}} and solve for {{{x}}}

{{{ (x -1)^2-25 =0 }}}

{{{ (x -1)^2 =25 }}}

{{{ sqrt((x -1)^2) =sqrt(25) }}}

{{{ x -1 =5 }}} or {{{ x -1 =-5 }}}

if {{{ x -1 =5 }}} => {{{ x =6 }}}

if {{{ x -1 =-5 }}} => {{{ x =-4 }}}


so, {{{x-intercepts}}} are at ({{{6}}},{{{0}}}) and ({{{-4}}},{{{0}}})


{{{drawing( 600, 600, -10, 10, -30, 10,circle(6,0,0.1),circle(-4,0,0.1),circle(1,-25,0.1),locate(1,-25,V(1,-25)), graph( 600, 600, -10, 10, -30, 10, x^2 - 2x -24)) }}}