When the expression $-5x^2+20x-17$ is written in the form $a(x+d)^2+e$, where $a$, $d$, and $e$ are constants, then what is the sum $a+d+e$?

thanks so much!

AnonymousConfusedGuy
Oct 22, 2017

#2**+3 **

-5x^2+20x-17 divide through by - 5

-5 ( x^2 - 4x + 17/5)

Take 1/2 of 4 = 2.......square it = 4.....add it and subtract it

-5 ( x^2 - 4x + 4 + 17/5 - 4)

Factor the first three terms and simplify

-5 [ (x -2)^2 + 17/5 - 20/5 ]

-5 [ (x - 2)^2 - 3/5]

-5( x - 2)^2 + 3

a = -5 d = -2 and e = 3

So

a + d + e = -5 + (-2) + 3 = -7 + 3 = - 4

CPhill
Oct 22, 2017