Question

How do you write the equation of the parabola in vertex form given vertex (3, -2), point (2, 3)?

Answer 1

`y=5(x-3)^2-2`

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)=(3,-2)`

`rArry=a(x-3)^2-2`

`"to find a substitute "(2,3)" into the equation"`

`3=a-2rArra=5`

`rArry=5(x-3)^2-2larrcolor(red)" in vertex form"`
graph{5(x-3)^2-2 [-10, 10, -5, 5]}