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

2 Answers
May 10, 2015

#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))#

May 10, 2015

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