The following three points are produced by some quadratic function of the form :
f(x) = Ax^2 + Bx + C
where A; B and C are real numbers and A = 0; they are (1/2,0);(0,10); and (4,0). Find a quadratic
function that satisfy�es these three points.
Form the igven points, you see that at x = 1/2 and at x = 4 the function is zero. This means that the function is proportional to:
(x - 1/2) (x - 4)
So, we can put:
f(x) = D (x - 1/2) (x - 4)
To find D, you use that at f(0) = 10:
f(0) = 2 D = 10 ----->
D = 5
Therefore:
f(x) = 5 (x - 1/2) (x - 4) =
5 x^2 - 45/2 x + 10