Question

Put this equation into vertex form.

Answer 1

Explanation:

So here the quadratic is in the factored form which is

`y = a(x - p)(x - q)`

where p and q are the zeroes of the function

In this case,

`p = 0`

`q = 7.7`

The vertex form is

`y = a(x - h) { \\ }^(2) + k`

The. x coordinate of the vertex lies between the two zeroes.

So

`h = (p + q)/(2)`

`k = f(h)`

`a = - 0.4`

So

`h = (7.7)/(2) = 3.85`

`k = f(3.85) = - (1)/(2.5) (3.85)( - 3.85) = 5.929`

So

The vertex form is

`- 0.4(x - 3.85) { }^(2) + 5.929`