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Which statements about the graph of the function f(x) = -x² - 4x + 2 are true?
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here, a=-1, b=-4,c=2

when we calculate,

we see that discriminant(D) is b²-4ac

on solving,

-4²-4*-1*2

16+8

24

as a<0, of it, is negative, the graph has a downward parabola.

D is positive, so the graph intersects the x axis at two points, whoch would be the roots and can be calculated by:

-b+√D

--------- ,(Root 1)

2a

-b-√D

-------- (Root 2)

2a

If a vertex is given(The point where the graph turns), then you can check by (-b/2a, -D/4a)
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