Question

How do you write the equation of the parabola in vertex form given vertex is (2,3) and the zeros are x=0 and x=4?

Answer 1

`y=-3/4(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 either of the 2 zeros into the equation"`

`"using " (4,0)`

`0=a(4-2)^2+3`

`rArr4a+3=0rArra=-3/4`

`rArry=-3/4(x-2)^2+3larrcolor(red)" in vertex form"`
graph{-3/4(x-2)^2+3 [-10, 10, -5, 5]}