Question

What is the equation of the parabola that has a vertex at `(2, 11)` and passes through point `(7,-4)`?

Answer 1

`y=-3/5(x-2)^2+11`

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)=(2,11)`

`rArry=a(x-2)^2+11`

`"to find a substitute "(7,-4)" into the equation"`

`-4=25a+11rArr25a=-15rArra=-15/25=-3/5`

`rArry=-3/5(x-2)^2+11larrcolor(red)"in vertex form"`