Question

Question #d0d05

Answer 1

`16x+40y-5y^2=48`

Explanation:

If the axis of symmetry of a parabola is parallel to the X-axis then the vertex form of the equation is
`color(white)("XXX")x=m(y-b)^2+a` with the vertex at `(a,b)` for some constant `m`

Given the vertex at `(-2,4)`
this becomes
`color(white)("XXX")x=m(y-4)^2+(-2)`

Since this equation has a solution `(x,y)=(3,8)`
we have
#color(white)("XXX")3=m(8-4)^2-2 #color(white)("XXX")16m=5
#color(white)("XXX")m=5/16

So the equation is
`color(white)("XXX")x=5/16(y-4)^2-2`

Which could be simplified in various forms:
`color(white)("XXX")16x=5(y^2-8y+16)-32`

`color(white)("XXX")16x=5y^2-40y+48`

`color(white)("XXX")16x+40y-5y^2=48`
graph{16x+40y-5y^2-48=0 [-4.07, 8.414, 2, 8.5]}