SOLUTION: What does it mean when it says "find the quadratic equation where f(1)=2 and the maximum value of f is f(3)=-5"?

Question 147835: What does it mean when it says "find the quadratic equation where f(1)=2 and the maximum value of f is f(3)=-5"?
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
A quadratic function has a general form of

A quadratic function has a maximum value where its derivative equals 0.
The derivative of f(x) is,

So now add your values that you know,

1.
and for the maximum value,

2.
Generally, you need three points to solve for a quadratic equation.
We can solve for the other two variables in terms of one variable.
From eq. 2,
2.

Then from eq.1,
1.

So the general form of the solution is,

There are some limits on a also.
Since the value at x=3 is a maximum, then a<0.

Here are three graphs for a=-.5,-1,-2 just to give a sense of the family of solutions.
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