Question

How do you solve `y=-1/2(x+4)^2+4`?

Answer 1

`x=-4+-2sqrt2`

Explanation:

`"set "y=0" to solve for x"`

`rArr-1/2(x+4)^2+4=0larrcolor(blue)"subtract 4 from both sides"`

`rArr-1/2(x+4)^2=-4`

`"divide both sides by "-1/2`

`rArr(x+4)^2=(-4)/(-1/2)=8`

`color(blue)"take the square root of both sides"`

`sqrt((x+4)^2)=+-sqrt8larrcolor(blue)"note plus or minus"`

`rArrx+4=+-2sqrt2larrcolor(blue)"subtract 4 from both sides"`

`rArrx=-4+-2sqrt2larrcolor(red)"exact solutions"`