so start with y = -x^2 + 5x + 7
then complete the square:
= -(x^2 -5x -7)
= -(x^2 -5x + 4/25 - 7 -4/25)
= -( (x-2/5)(x-2/5) -7 -4/25)
= -(x-2/5)^2 -(7 4/25)
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factors are (x + 9)(x - 4) so x = 4 or -9. Does that help?
x2 + 5x - 120 can not be factored.
x2 + 5x + 6 = (x + 2)(x + 3)
The vertex is (-9, -62).
(x - 3)(x - 2)