Question 1111541
Something is missing. Is there a typo?
What was meant by "the tangent to the graph of f at the point (-1;7/2) is 3" is not obvious to me.
Is it that {{{3}}} is the slope of the tangent?
It could not be that {{{y=3}}} is the equation
of the straight line tangent to the graph at the point (-1,7/2),
because that line must contain the point (-1,7/2).
 
We are told {{{f(x)=-ax^2+bx+c}}} , and {{{f(-1)=-a(-1)^2+b(-1)+c=-a-b+c=7/2}}} .
The slope of the tangent to {{{f(x)=-ax^2+bx+c}}} at a point with any {{{x}}} is
{{{df/dx=-2ax+b}}} , the derivative of {{{f(x)}}} .
When {{{x=-1}}} , the value of the derivative is
{{{-2a(-1)+b=2a+b}}} .
 
If that slope is {{{3}}} ,
we have {{{system(-a-b+c=7/2,2a+b=3)}}} .
That system of equations has infinite solutions,
so there is no way to prove that a=1/2 and b=2 with
Knowing just that the tangent at (-1,7/2) has a slope of 3. 
{{{red(system(a=1/2,b=2,c=6))}}} is one of them, but {{{green(system(a=1,b=1,c=11/2))}}} and {{{blue(system(a=3/2,b=0,c=5))}}}
are also among the infinite number of solutions:
{{{drawing(300,300,-3,7,-1,9,
graph(300,300,-3,7,-1,9,-0.5x^2+2x+6,-x^2+x+5.5,-1.5x^2+5),
circle(-1,3.5,0.2),line(-3,-2.5,1,9.5)
)}}}
 
Another piece of information would give us another equation,
which could complete a system of equation with a unique solution.