Question

How do you write a quadratic equation with vertex; ( 0,1 ); point: ( 1,3 )?

Answer 1

`y=2x^2+1`

Explanation:

`"the equation of a quadratic function 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)=(0,1)`

`rArry=a(x-0)^2+1`

`rArry=ax^2+1`

`"to find a, substitute " (1,3)" into the equation"`

`rArr3=a+1rArra=2`

`rArry=2x^2+1larrcolor(red)" in vertex form"`
graph{2x^2+1 [-10, 10, -5, 5]}