Algebra II - Midterm

Question 1

how to find domain from a fraction

Answer 1

set denominator not equal to 0

Question 2

how to find domain from a radical

Answer 2

set radical greater than or equal to 0

Question 3

what is set notation

Answer 3

{x / 1 < x < 100}

Question 4

what is interval notation

Answer 4

(1,100)

Question 5

when the negative is on the outside of the equation, what transformation occurs

Answer 5

reflect over x (outside=x)

Question 6

when the negative is on the inside of the equation, what transformation occurs

Answer 6

reflect over y (inside=y)

Question 7

when a in f(x)=af(x-c)+d is a fraction, what transformation occurs

Answer 7

vertical compression

Question 8

when a in f(x)=af(x-c)+d is >1, what transformation occurs

Answer 8

vertical stretch

Question 9

how do you write a piecewise function

Answer 9

f(x)= {function domain}

Question 10

what is the axis of symmetry in vertex form? f(x)=a(x-h)^2+k

Answer 10

h

Question 11

what is the axis of symmetry in intercept form? f(x)=a(x-p)(x-q)

Answer 11

p+q/2 (halfway between p and q)

Question 12

how do you find the vertex in intercept form? f(x)=a(x-p)(x-q)

Answer 12

plug in axis of symmetry

Question 13

how do you find the axis of symmetry in standard form? f(x)=ax^2+bx+c

Answer 13

-b/2a

Question 14

how do you find the x-intercepts in standard form? f(x)=ax^2+bx+c

Answer 14

quadratic formula

Question 15

how do you find the y-intercept in standard form? f(x)=ax^2+bx+c

Answer 15

c

Question 16

how do you go from vertex/intercept form to standard form

Answer 16

FOIL

Question 17

how do you go from standard form to intercept form?

Answer 17

factor

Question 18

how do you go from standard form to vertex form

Answer 18

complete the square

Question 19

how do you do difference of squares

Answer 19

take sqrt of 1st term = a
take sqrt of 2nd term =b
(a+b) (a-b)

Question 20

how do you factor a trinomial

Answer 20

cross method

Question 21

how do you rationalize the denominator?
ex. 8/sqrt2

Answer 21

multiply the top and bottom by the radical
ex. 8sqrt2/2

Question 22

what is the conjugate of a binomial?

Answer 22

the inverse of a binomial
ex. 2+sqrt7 2-sqrt7

Question 23

what is i^2

Answer 23

-1

Question 24

what do you do to add/subtract complex numbers?
ex. (2+5i)-(3-2i)

Answer 24

combine like terms
ex. 2-3=-1 5i+2i=7i -1+7i

Question 25

what do you do to multiply complex numbers ex. (2+3i)(3-5i)

Answer 25

distributive property and treat i as variables. not fully simplified if i has an exponent >1

Question 26

what is the discriminant

Answer 26

b^2-4ac (inside of quadratic equation)

Question 27

when the discriminant is 0 how many solutions are there

Answer 27

1 rational solution

Question 28

when the discriminant is >0 how many solutions are there

Answer 28

2 solutions, rational if a perfect square

Question 29

when the discriminant is <0 how many solutions are there

Answer 29

2 imaginary solutions

Question 30

how do you complete the square ax^2+bx+c

Answer 30

isolate x^2+bx on one side and c on the other take (b/2)^2 and add to both sides of the equation factor for a perfect square take the sqrt of both sides

Question 31

what are the different ways to solve a quadratic equation? ex. x^2+2x=48

Answer 31

1. square root 2. factoring 3. completing the square 4. quadratic formula

Question 32

what makes a non-polynomial

Answer 32

1. exponents that are not whole numbers 2. sqrt of x 3. negative exponents 4. fractions with x underneath 5. x in the exponent

Question 33

how do you divide a polynomial

Answer 33

1. long division (treat like regular long division) 2. synthetic division

Question 34

what is the equation for difference of squares a^2-b^2

Answer 34

(a+b)(a-b)

Question 35

what is the equation for the sum of cubes a^3+b^3

Answer 35

(a+b)(a^2-ab+b^2)

Question 36

what is the equation for the difference of cubes a^3-b^3

Answer 36

(a-b)(a^2+ab+b^2)

Question 37

how do you factor a polynomial with 4 terms

Answer 37

factor by grouping

Question 38

what is the remainder theorem

Answer 38

if the polynomial P(x) is divided by x-c, the remainder is P(c) use synthetic division to divide and the remainder is the solution

Question 39

what is the factor theorem

Answer 39

if the remainder comes out to be 0, then x-c is a factor of P(x)

Question 40

what is the rational zero test

Answer 40

factors of p/factors of q p=constant term q=leading coefficient use synthetic division to see which zeros are correct

Question 41

how many real zeros does a function have

Answer 41

whatever its degree is

Question 42

how many relative max/min does a function have

Answer 42

degree-1

Question 43

what will the end behavior of an even degree and positive leading coefficient look like ex. x^4-11x^3+42x^2-64x+32

Answer 43

^ ^ I I | |

Question 44

what will the end behavior of an odd degree and a positive leading coefficient look like ex. x^7+2x^3-5x^2+2

Answer 44

I ^ v I

Question 45

what will the end behavior of an even degree and negative leading coefficient look like ex. -2x^4+3x^2-5

Answer 45

I I V V

Question 46

what will the end behavior of an odd degree and negative leading coefficient look like ex. -x^7+2x^2+3x-4

Answer 46

^ I I V

Question 47

what is the multiplicity of a zero

Answer 47

the exponent on its factor ex. (x+1)^2 is 2 determines how the graph will cross the x axis

Question 48

if the multiplicity is 1 how will it pass the x axis

Answer 48

pass through

Question 49

if the multiplicity is odd how will it pass the x axis

Answer 49

squiggle (cubic)

Question 50

if the multiplicity is even how will it pass the x axis

Answer 50

bounce (parabola)

Question 51

if a+sqrt b is a zero, what is the other zero

Answer 51

a-sqrt b