Question

Find a polynomial p of degree 2 so that

p(1) = 2,
p(2) = 13,
p(4) = 47,

Answer 1

The first step is always the hardest...
Since it is a polynomial, with degree 2, that means it's a quadratic.
so\[ p(x)=ax^2 + bx + c \]
When p(1)=2, it means
when x=1, p(x)=2.
Solve the simultaneous eqs.