exam 2

Question 1

what is the function of a quadratic?

Answer 1

ax^2+bx+c

Question 2

what movements can a quadratic do?

Answer 2

vertical flip
stretch
shift up/down
shift left/right

Question 3

find the roots of x^2-4x+3

Answer 3

(x-3)(x-1)
x= 3,1

Question 4

what is vertical form?

Answer 4

C(x-a)^2+k

Question 5

what is the general method of completing the square?

Answer 5

find half the coefficient (b/2)
add and subtract (b/2)^2 to the quadratic
break down the perfect square and add y-intercept

Question 6

define discriminant

Answer 6

the term under the square root in the quadratic formula

Question 7

what is a discriminant is negative? positive? zero?

Answer 7

neg- no real roots
pos- 2 roots
0- 1 root

Question 8

what is the degree of a polynomial?

Answer 8

the highest power that occurs

Question 9

what is a rational function?

Answer 9

a fraction of 2 polynomials

Question 10

what is discontinuity

Answer 10

spots where the graph has a break, can be a vertical asymptote or a removable discontinuity

Question 11

what are dominating terms

Answer 11

the highest degree of a function

Question 12

what are the 3 cases for rational functions

Answer 12

if y –> 0, n<m
if y –> (-)infinity, n>m
if An/Bm, n=m

Question 13

what does the end behavior depend on?

Answer 13

if the numerator or denominator has a higher degree

Question 14

define horizontal asymptote

Answer 14

if f(x) approaches k as x moves to (-)infinity, then y=k.

Question 15

define direct proportionality

Answer 15

quantity A is proportional to B if A=Bk for any nonzero k.

Question 16

define inverse proportionality

Answer 16

as A gets larger, B gets smaller; if A=k/B for any nonzero k

Question 17

define power functions

Answer 17

if y is proportional to x^a, then y=kx^a for nonzero constants k and a

Question 18

i= ?

Answer 18

square root of -1