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# 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\$?

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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
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AnonymousConfusedGuy  Oct 22, 2017
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-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

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