The question is f(x)=-2x^2-8x+5.

I worked as hard as I could and couldn't come to factors that added to 4 and multiplied to 2.5 so I went ahead and checked a graphing calculator. It gave me x=(-4.55) and x=(.55). My question there, is how I would ever come to those two answers on my own without the use of a calculator?

Now for the vertext, I'll show my work and the answer that I got (which I now know is wrong because of the graphing calculator).

-2x^2-8x+5

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

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

-2(x^2+4x+4)-8+5

-2(x+2)^2-3

Therefore, the point of vertex is (-2, -3).

The graphing calculator has the vertex at (-2, 13). I tried to get that number myself, but I'm not sure where I went wrong. Can anyone explain or show you work of how those numbers are attained? Thank you!