Question

How do you write `y = -4x^2 + 8x + 60` into vertex form?

Answer 1

`y = -4x^2+8x+60 = -4(x-1)^2 + 64`.

As I mentioned on another answer:

In general, for `y = ax^2 + bx + c`, the `x` coordinate of the vertex is `-b/(2a)`, and the vertex form is:

`y = a(x + b/(2a))^2 + (c - b^2/(4a))`

Answer 2

Another way:
Vertex form:
`f(x) = a(x -b/(2a))^3 + f(-b/(2a))`

-b/2a = -8/-8 = 1

f(1) = -4 + 8 + 60 = 64

Vertex form: `y = -4.(x - 1)^2 + 64`

Check:
#Develop f(x) = -4(x - 1)^2 + 64 = -4(x^2 - 2x + 1) + 64 = -4x^2 + 8x - 4 + 64 = -4x^2 + 8x + 60# Correct