Question

How do you write the equation of the parabola in vertex form given Vertex: (4, 4); point: (0, 0)?

Answer 1

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

Explanation:

`"the equation of a parabola in "color(blue)"vertex form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))`

`"where "(h,k)" are the coordinates of the vertex and a"`
`"is a multiplier"`

`"here "(h,k)=(4,4)`

`rArry=a(x-4)^2+4`

`"to find a substitute "(0,0)" into the equation"`

`0=16a+4rArra=-4/16=-1/4`

`rArry=-1/4(x-4)^2+4larrcolor(red)"in vertex form"`
graph{(y+1/4x^2-2x)((x-4)^2+(y-4)^2-0.04)=0 [-10, 10, -5, 5]}