When the expression -5x^2 + 20x - 17 + 3x^2 + 12x - 8 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?
+133 Combine like terms.
-2x^2 + 32x - 25
Factor out a -2.
-2(x^2 - 16x) - 25
Complete the square.
-2(x^2-16x+64) - 25 + ?
To balance the equation, ? = 2x64 = 128.
Thus, our answer is -2(x-8)^2 + 103, so -2-8+103 = 93.
