SOLUTION: I am tring to do the final worksheet of the term and I just don't understand it well enough to take the final. If anyone can help me with these equations I would really appreciate

You can put this solution on YOUR website!
First we will factor:
f(x)=-(x+3)(2x-1).
Find the intercepts first:
y-intercept:
f(0)=-(3)(-1)=3. That gives (0,3).
x-intercepts:
0=-(x+3)(2x-1) implies x=-3 or x=1/2. That gives (-3,0) and (1/2,0)
Now, the x-coordinate here will be -b/2a where f(x)=ax^2+bx+c. Thus, x=5/(-4)=-4/5 will be the x-coordinate of the vertex. Plug this in to get the y value: f(-4/5)=-2(16/25)-5(-4/5)+3=-32/25+175/25=143/25; So, (-4/5,143/25).
Note that this will be concave down because the coefficient of the x^2 term is negative.