MathDB

Let

b

and

c

be fixed real numbers and let the ten points

(j,y_j )

for

j=1,2,\ldots,10

lie on the parabola

y =x^2 +bx+c.

For

j=1,2,\ldots, 9

let

I_j

be the intersection of the tangents to the given parabola at

(j, y_j )

and

(j+1, y_{j+1}).

Determine the poynomial function

y=g(x)

of least degree whose graph passes through all nine points

I_j .

A1