Pre-Calculus Mrs. Spatola
Name______Date______
Homework – Polynomials
1) Determine the maximum number of turning points of f.
f(x) = (x - 2)2(x + 5)2
2) Write the function in vertex form. Find its vertex, axis of symmetry, and intercepts.
f(x) = 2x2 + 8x + 13
3) Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.
f(x) = 3x2 - 2x – 6
4) Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.
f(x) = -11x2 - 2x - 6
5) The profit that the vendor makes per day by selling x pretzels is given by the function Find the number of pretzels that must be sold to maximize profit.
6) The owner of a video store has determined that the profits P of the store are approximately given by where x is the number of videos rented daily. Find the maximum profit to the nearest dollar.
7) Find a polynomial that has the given zeros. (There are many correct answers.)
a) 0, 4, 3
b) ,
8) Write the function in vertex form.
9) Identify the right-hand and left-hand behavior of the graph of the polynomial function.
10)
10) Identify the right-hand and left-hand behavior of the graph of the polynomial function.
11)
11) Write the function in vertex form. Identify the vertex, axis of symmetry and the x-intercepts.
12)State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
f(x) =
13) State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
f(x) =6(x - 1)11(x + 1)5
f(x) = -10x5 + x4 +
14)Form a polynomial whose zeros and degree are given.
Zeros: 3, multiplicity 2; -3, multiplicity 2; degree 4