Question

How do you find the vertex and intercepts for `2(x-3)^2=6y+72`?

Answer 1

`"see explanation"`

Explanation:

`"expressing in translated form"`

`•color(white)(x)(x-h)^2=4p(y-k)`

`"where "(h,k)" are the coordinates of the vertex and p"`
`"is the distance betwee the vertex and the focus/directrix"`

`rArr2(x-3)^2=6(y+12)`

`rArr(x-3)^2=3(y+12)larrcolor(blue)"in translated form"`

`rArrcolor(magenta)"vertex "=(3,-12)`

`"to obtain the intercepts"`

`• " let x = 0, in the equation for y-intercept"`

`• " let y = 0, in the equation for x-intercepts"`

`x=0to9=3y+36rArry=-9larrcolor(red)"y-intercept"`

`y=0to(x-3)^2=36`

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

`rArrx-3=+-sqrt36larrcolor(blue)"note plus or minus"`

`rArrx=3+-6`

`rArrx=-3,x=9larrcolor(red)"x-intercepts"`