To Write :
[tex]y = 6x^2 + 18x + 14[/tex] in the form [tex]y = a(x -h)^2 + k[/tex] ?
Solution :
[tex]y = 6x^2 + 18x + 14\\\\y = (\sqrt3 x)^2+(2\times \sqrt{3}\times 3\sqrt{3} )x +(3 \sqrt{3} )^2- (3 \sqrt{3} )^2+14=0\\\\y = ( \sqrt{3}x+ 3\sqrt{3})^2+14-27 =0\\\\y = ( \sqrt{3}x+ 3\sqrt{3})^2 - 13 =0\\\\y= 3(x + 3)^2-13=0[/tex]
Therefore, this is the simplified form.
