Find the quadratic polynomial f(x) such that f(0) = 3, f(1) = -5, and f(2) = 7.
Let the quadratic be in the form \(ax^2 + bx +c\).
Subsituting in \(x = 0\) gives us: \(0a + 0b + c= 3 \), or effectively, \(c = 3\)
Subsituting in \(x = 1\) and \(c = 3\) gives us: \(a + b + 3 = -5\)
Repeating the same process for \(x = 2\) gives us: \(4a + 2b + 3 = 7\)
Now, we have to solve for a and b, and subsitute these into the original quadratic.
Can you take it from here?