Unit 7 and 8 Exam

Question 1

how to factor cubic expressions, short

Answer 1

use sum/difference of x formula
(a+b)(a^2-ab+b^2)
(a-b)(a^2+ab+b^2)
simplify

Question 2

how to factor cubic expressions, long

Answer 2

split equation in two
find GCF of both sides
one side will be the remainder of factoring from previous step
other side will be the numbers factored out

Question 3

even, odd, or neither?

Answer 3

replace x with -x and simplify
if it remains the same, even
if changes to opposite sign, odd
if neither, neither

Question 4

find degree

Answer 4

highest degree

Question 5

find degree of y=a(x+…)(x+…)(x+…)

Answer 5

add all degrees of all x

Question 6

end behavior

Answer 6

x -> ∞, f(x) -> …
x -> -∞, f(x) -> …

Question 7

end behavior of odd function

Answer 7

ends go in opposite directions

Question 8

end behavior of even function

Answer 8

ends go same direction

Question 9

how to tell end behavior from leading coefficient

Answer 9

if negative
right goes down, left goes up (if odd degree)
both go down (if even degree)

if positive
left goes down, right goes up (if odd degree)
both go up (if even degree)

Question 10

number of zeros?

Answer 10

degree

Question 11

number of turns?

Answer 11

degree - 1

Question 12

quadratic formula

Answer 12

x = -b +- √b^2 - 4ac
________________
2a

Question 13

x intercepts when y = k(x−a)(x−b)(x−c)

Answer 13

set x as 0 and solve

Question 14

synthetic divison?

Answer 14

set up only coefficients (flip sign of divisor)
drop first number
multiple divisor by dropped number
put number under second coefficient
add
multiply divisor by new added number
repeat until remainder

if remainder ≠ 0
divide by original divisor (entire divisor, not just coefficient)

Question 15

how to look find equation from graph

Answer 15

y = k(x−a)(x−b)(x−c)
number of sets of parenthesis is determined by degree (turns plus 1)
a, b and c are roots