Question

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.

Answer 1

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