Posted by **Johnny** on Friday, October 15, 2010 at 9:38am.

identify the vertex of the parabola y=4x2-40x+96

- Math ( not J&W) -
**Reiny**, Friday, October 15, 2010 at 9:54am
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((x-5)^2 - 25) + 96

= 4(x-5)^2 - 100 + 96

=4(x-5)^2 - 4

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