Find a polynomial function whose graph passes through (-1,1),(0,7),(1,7), and (2,7).

Question



Answer 1

y = x (x-1) (x-2) + 7

Subtract 7 from each of the points to find where a shifted-down version of the function has zeros. Use those zeros to make the preliminary polynomial. Plug in the shifted down first point [(-1, 1) => (-1, -6)] to check if anything else is needed. Since it is not, one just adds 7 to the polynomial from earlier and that's that.