f(x) is a monic polynomial such that f(0)=4 and f(1)=-10. If f(x) has degree 2, what is f(x)? Express your answer in the form ax^2+bx+c, where a, b, and are real numbers.
+23246 The general polynomial function of degree 2 can be written as: ax2 + bx + c = y
Since it is a monic polynomial: a = 1 ---> 1·x2 + bx + c = y
---> x2 + bx + c = y
f(0) = 4 ---> x = 0 and y = 4 ---> (0)2 + b·(0) + c = 4 ---> c = 4
f(1) = -10 ---> x = 1 and y = -10 ---> (1)2 + b(1) + 4 = -10 ---> b = -15
Since a = 1 and b = -15 abd c = 4 ---> x2 - 15x + 4 = y
