+921 Determine the range of the function $(x) = -4x^2-8x-6 + 3x^2 - 17x + 10. Enter your answer in interval notation.
+37165 First, reduce/simplify the quadratic to:
-x^2 -25x +4 This is a dome shaped parabola
put it into vertex form to find the highest point
-1 ( x^2 + 25x) = y -4
-1 ( x+12.5)^2 = y-4 - 156.25
-1 ( x+12.5)^2 = y + 160.25 shows vertex is -12.5, 160.25
So the y-values this parabola can have ( the range) is ( - inf, 160.25]
