To graph y = (x - 3 )2 + 1, shift the graph of y = x 2 to the right __ units and then __ 1 unit. (pp. 252-260)

Summary of results from sections 4.1-4.3 VECTOR SPACE AND ITS DEFINITION A vector space consists of the following four components A set of vectors V A set of scalars F (either the set of all real numbers R or the set of all complex numbers C). A rule for adding vectors in V: A rule for multiplying vectors in V: Then V is a vector space over F with addition and multiplication if the following 10 axioms (A1 ▯ A10) hold. Axiom 1 Closure under addition: For each pair of vectors u and v in V , the sum u + v is also in V . Axiom 2 Closure under scalar multiplication: For each vector v in V , and each scalar k, the scalar multiple kv is also in V . Axiom 3 Existence of a zero vector in V : In V there is a vector, denoted by 0 and called the zero vector, satisfying