k=7 and you done!
Find the quadratic function f such that f (2) = f (4) = 0 and 7 is the greatest value of f (x).
I know that
because the parabola is a negative one because it has a greatest value and because the x ints are 2 and 4
I don't know what to do from here
A better solution:
Your intercepts are at and , so the axis of symmetry is So the turning point is .
Therefore the equation of the parabola is:
.
Now substituting another of your points that lie on the curve, e.g. , you find
.
So the equation of your parabola is:
.
Yet another way to do this if you don't happen to know off-hand that the vertex is always exactly midway between the x-intercepts: . Now complete the square to find the highest point:
Since a square is never negative will have its lowest point (and its highest) when, just as Prove It said, when x= 3. At that point .