Warm Up
1. Write the function rule for a quartic polynomial going through (2,0), (5,0), (­3,0), (­1,0) and (0,6) without the use of your calculator.
2. Write in standard form. (2x2 + 7x ­ 3)(x2 + 5x)
A little review...
Does the point you plug into your function rule in order to find the correct coefficient value (k or a) need to be the y­intercept of the graph?
1) Yes, we need to know where the graph starts.
2) Yes, we need to know how far up the graph is shifted.
3) No, we need to know the x­intercepts.
4) No, we need only one other point on the graph.
What step in writing a function rule by hand do you get stuck on or need more help with?
1) Getting started
2) Deciding which factor should be repeated
3) Finding the coefficient value (k or a)
4) None, I am a master!
P(x) is a polynomial of degree m.
T(x) is a polynomial of degree n.
What is the degree of the polynomial P(x)T(x)?
A) The larger of m and n.
B) It depends on what P(x) and T(x) are.
C) m + n
D) mn
In which of the following cases will the degree of the polynomial function not be equal to the number of its zeroes?
2
I. f(x) = (x ­ a)(x ­ b)
A) I and IV
II. g(x) = (x ­ a)(x ­ b)(x ­ c)(x ­ d) B) I, III, and IV
III. h(x) = (x ­ a)2(x ­ b)2
C) II and V
3
IV. k(x) = (x ­ a) (x ­ b)
D) II, III, and V
V. m(x) = (x ­ a)(x ­ b)(x ­ c)
Clickers #1-5
Find x­int
Find Vertex
Vertex Form f(x) = a(x ­ h)2 + k Find y­int
Clickers #6-9
Standard Form
g(x) = ax2 + bx + c
Factored Form h(x) = k(x ­ r)(x ­ s) Vertex Form f(x) = a(x ­ h)2 + k Pg 350 #4
2
x + 6x + 11
#7
Clickers #10