Question

How do you find the quadratic function with vertex (2,3) and point (0,2)?

Answer 1

`y=-1/4(x-2)^2+3`

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)=(2,3)`

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

To find a, substitute the point (0 , 2) into the equation.

`rArr2=4a+3rArra=-1/4`

`rArry=-1/4(x-2)^2+3" is the quadratic function"`