Question

How do you write a quadratic function in vertex form whose graph has the vertex (2,-4) and point (0,0)?

Answer 1

`y=(x-2)^2-4`

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 vertex "=(2,-4)=(h,k)`

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

`"to find a substitute "(0,0)" into the equation"`

`0=4a-4rArra=1`

`rArry=(x-2)^2-4larrcolor(red)" in vertex form"`
graph{(x-2)^2-4 [-10, 10, -5, 5]}