Question

How do you write the quadratic function in vertex form given vertex (2,-1) and point (4,3)?

Answer 1

`y=(x-2)^2-1`

Explanation:

`"the vertex form of a quadratic function 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)=(2,-1)`

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

`"to find a, substitute the point "(4,3)" into the equation"`

`rArr3=a(4-2)^2-1`

`rArr4a=4rArra=1`

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