SOLUTION: How do i prove values of a=1/2 and b=2, if given f(x)=-ax^2+bx+c and the tangent to the graph of f at the point (-1;7/2) is 3

Question 1111541: How do i prove values of a=1/2 and b=2, if given f(x)=-ax^2+bx+c and the tangent to the graph of f at the point (-1;7/2) is 3
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
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 is the slope of the tangent?
It could not be that 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 , and .
The slope of the tangent to at a point with any is
, the derivative of .
When , the value of the derivative is
.

If that slope is ,
we have .
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.
is one of them, but and
are also among the infinite number of solutions:

Another piece of information would give us another equation,
which could complete a system of equation with a unique solution.
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