quadratic function/inequality, multi-step problem and I am stuck

Hi everyone, happy Tuesday!

I am taking algebra and I just don't get quadratics. I have a sheet of different quadratic questions I have been working on since yesterday, trying to figure it out before coming here, but I failed :(

I have a couple questions below, thank you in advance for your help :)

2. f(x)=2+5x-3x^2

a. determine if it goes up or down..... down I got that far :)

b. find the vertex, this is where I got stuck

c. find axis of symmetry

d. find x- and y- intercepts

e. sketch the graph y=f(x)

f. determine whether the function has a maximum value or a minimum value, then find this value (What, I am so lost!)

g. find the range of f.

ahh why are there so many questions for one function!

3.) I am stuck on this one because the fractions killed me, er

solve the quadratic inequality:

1/2x^2 - 3/4x + 7 <(or equal, didn't know how to add the bar under) 0