[tex]y = - 3(x - 2) ^{2} + 4[/tex]
[tex]y = - 6x + 16[/tex]
distribute the -3 and the square into the first equation
[tex]y = - 3x ^{2} + 12x - 8[/tex]
[tex]y = - 6x + 16[/tex]
multiply the second equation by 2
[tex]y = - 3x ^{2} + 12x - 8[/tex]
[tex]y = - 12x + 32[/tex]
add the equations together
[tex]y = - 3x ^{2} + 24[/tex]
factor out -3
[tex]y = - 3(x ^{2} - 8)[/tex]
factor inside parenthesis
[tex]y = - 3(x + \sqrt{8} )( x - \sqrt{8}) [/tex]
refine
[tex]y = - 3(x + 2 \sqrt{2} )(x - 2 \sqrt{2} )[/tex]
