J&W
posted by Johnny on .
identify the vertex of the parabola y=4x240x+96

several ways to do this.
quickest way:
the x of the vertex is b/(2a)
= (40)/8 = 5
sub back into equation
y = 4(25) 40(5) + 96 = 4
vertex (5,4)
calculus way:
dy/dx = 8x  40 = 0
x = 5
proceed as above
completing the square:
y = 4x^2  40x + 96
= 4(x^2  10x + 25  25 + 96
= 4((x5)^2  25) + 96
= 4(x5)^2  100 + 96
=4(x5)^2  4