Consider the transformation T(ax^2 + bx + c) = 2ax + b of P2 → P1.

Question

(a) Find T((ax^2 + bx + c) + (px^2 + qx + r)).

(b) Find T(k(ax^2 + bx + c)).

(c) Find the image of 3x^2 − 2x + 1.

(d) Determine another element of P2 that has the same image.

Answer 1

(a) Find T((ax^2 + bx + c) + (px^2 + qx + r)).

(b) Find T(k(ax^2 + bx + c)).

(c) Find the image of 3x^2 − 2x + 1.

(d) Determine another element of P2 that has the same image.

Answer 2

a) 2ax+2px+b+q
b) k(2ax+b)
c) 6x-2
d) 3x^2-2x+6