Problems on synth division, zeros, quads...

Hi all,

I've been struggling with these problems all day. Any help would be appreciated.

This one I think I got right, but if anyone could just double check, thatd be nice!

1)Find the vertex, x-intercepts, and equation in standard form

f(x) = -x^2 - 5x - 6

My answers:

Vertex: (-2.5, 0.25)

X Ints: (-3,0) (-2,0)

f(x)= -(x+2.5)+0.25

Number 2, I tried, and THOUGHT I knew, but apparently I don't.

2) Find the equation of a parabola that has the vertex (2, -1) and goes through the point (2, -2)

My answer:

F(X)= -3/4(X+2)^2 + 1

Apparently this is wrong as it does not pass through the given point.

And these I tried but did not get even close: (I did synthetic division last year but they dont explain how to do it in my book!)

3) Use synthetic division

(3x^4 + 7x^3 - 7x + 2) divided by (3x-2)

4) Find the zeros for:

a) F(X)= x^3 - 11x +150

b) F(X)= 2x^4 -5x^3 -10x -12

5) Find the factored form of the equation: f(x)=2x^3 + 11x^2 +12x - 9

One of the answers I got (there should be 3?): (X+3)

If anyone could help me with these I'd greatly appreciate it! Thanks!