Question 821147
That is a misunderstanding.
Vertex form IS standard form.  
You could put #1 into GENERAL form through multiplying and simplifying.
{{{f(x)=-(3/4)(x^2+4x+8)+8}}}
{{{f(x)=(-3/4)x^2-3x-6+8}}}
{{{highlight_green(f(x)=(-3/4)x^2-3x+2)}}}


#2,
Only a small amount of help to start with #b,
Factor the right hand side:
{{{y=-2(x^2-14x+7/2)}}}
The missing square piece is {{{(-14/2)^2=49}}};
ADD and SUBTRACT 49 INSIDE the parenthesised quadratic expression, and simplify but adjusting the form into {{{a(x-h)^2+k}}};
Can you perform the necessary steps or do you still need help?