Chapter 3

Question 1

quadratic form

Answer 1

f(x)=ax^2+bx+c

Question 2

standard form

Answer 2

f(x)=a(x-h)^2+k

Question 3

intercept form

Answer 3

f(x)=a(x-p)(x-q)

Question 4

quadratic form a.o.s.

Answer 4

-b/2a

Question 5

quadratic form vertex

Answer 5

(-b/2a, f(-b/2a))

Question 6

standard form a.o.s.

Answer 6

h

Question 7

standard form vertex

Answer 7

(h, k)

Question 8

intercept form a.o.s.

Answer 8

(p+q)/2

Question 9

intercept form vertex

Answer 9

((p+q)/2, f((p+q)/2))

Question 10

End Behavior:
Positive Even

Answer 10

Field Goal

Question 11

End Behavior:
Negative Even

Answer 11

Rainbow

Question 12

End Behavior:
Positive Odd

Answer 12

Up towards the right
Down towards the left

Question 13

End Behavior:
Negative Odd

Answer 13

Down towards the right
Up towards the left

Question 14

number of positive real zeros
(Descarte’s Rule of Signs)

Answer 14

Number of variations in signs of P(x) or less by an even whole number

Question 15

number of negative real zeros
(Descarte’s Rule of Signs)

Answer 15

Number of variations in signs of P(-x) or less by an even whole number

Question 16

Upper bound

Answer 16

Divide P(x) by x-b (b>0) using synthetic division and if the row has no negatives, b is an upper bound

Question 17

Lower Bound

Answer 17

Divide P(x) by x-b (b<0) using synthetic division and if the row have alternately positive and negatives, b is a lower bound

Question 18

Fundamental Theorem of Algebra

Answer 18

Every polynomial with complex coefficients has at least one complex zero

Question 19

Multiplicity

Answer 19

If the factor x-c appears k times, we say c is a zero of multiplicity k

Question 20

Zeros Theorem

Answer 20

Every polynomial of degree n>1 has exactly n zeros

Question 21

Complex Zeros Theorem

Answer 21

If the polynomial P has real coefficients, and if the complex number z is a zero of P, then its complex conjugate is also a zero of P

Question 22

Linear and Quadratic Factors Theorem

Answer 22

Any polynomial with real coefficients can be factored into a product of linear and quadratic factors with real coefficients