We need to determine the shape of the given conic section using its equation.
We know that, for the general equation of conic section
For the given equation,
The graph of the parabola has been shown below.
Let L : P2 P3 be a linear transformation for which we
know that L(1) = 1, L(t) = t 2, L(t 2) = t 3 + t.
(a) Find L(2t 2 - 5t + 3). (b) Find L(at 2 + bt + c).