Question

What is the equation of the parabola that has a vertex at `(2, -5)` and passes through point `(-8,-7)`?

Answer 1

`y=-1/50(x-2)^2-5`

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,-5)`

`rArry=a(x-2)^2-5`

`"to find a substitute "(-8,-7)" into the equation"`

`-7=100a-5`

`rArra=-1/50`

`rArry=-1/50(x-2)^2-5larrcolor(red)" in vertex form"`

`"distributing and collecting like terms"`

`y=-1/50x^2+2/25x-127/25larrcolor(red)" in standard form"`