Question

What is the equation of the parabola that has a vertex at `(1, -4)` and passes through point `(2,-6)`?

Answer 1

`y=-2x^2+4x-6`

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 constant.

`"here "(h,k)=(1,-4)`

`rArry=a(x-1)^2-4`

`"to find a substitute "(2,-6)" into the equation"`

`-6=a-4rArra=-2`

`rArry=-2(x-1)^2-4larrcolor(red)" in vertex form"`

`rArry=-2x^2+4x-6larrcolor(red)" in standard form"`