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Scholars Classes Flashcards > Algebra II - Midterm > Flashcards

Algebra II - Midterm Flashcards

1
Q

how to find domain from a fraction

A

set denominator not equal to 0

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2
Q

how to find domain from a radical

A

set radical greater than or equal to 0

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3
Q

what is set notation

A

{x / 1 < x < 100}

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4
Q

what is interval notation

A

(1,100)

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5
Q

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

A

reflect over x (outside=x)

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6
Q

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

A

reflect over y (inside=y)

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7
Q

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

A

vertical compression

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8
Q

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

A

vertical stretch

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9
Q

how do you write a piecewise function

A

f(x)= {function domain}

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10
Q

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

A

h

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11
Q

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

A

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

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12
Q

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

A

plug in axis of symmetry

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13
Q

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

A

-b/2a

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14
Q

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

A

quadratic formula

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15
Q

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

A

c

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16
Q

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

A

FOIL

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17
Q

how do you go from standard form to intercept form?

A

factor

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18
Q

how do you go from standard form to vertex form

A

complete the square

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19
Q

how do you do difference of squares

A

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

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20
Q

how do you factor a trinomial

A

cross method

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21
Q

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

A

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

22
Q

what is the conjugate of a binomial?

A

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

23
Q

what is i^2

A

-1

24
Q

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

A

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

25
Q

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

A

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

26
Q

what is the discriminant

A

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

27
Q

when the discriminant is 0 how many solutions are there

A

1 rational solution

28
Q

when the discriminant is >0 how many solutions are there

A

2 solutions, rational if a perfect square

29
Q

when the discriminant is <0 how many solutions are there

A

2 imaginary solutions

30
Q

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

A

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

31
Q

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

A
  1. square root
  2. factoring
  3. completing the square
  4. quadratic formula
32
Q

what makes a non-polynomial

A
  1. exponents that are not whole numbers
  2. sqrt of x
  3. negative exponents
  4. fractions with x underneath
  5. x in the exponent
33
Q

how do you divide a polynomial

A
  1. long division (treat like regular long division)
  2. synthetic division
34
Q

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

A

(a+b)(a-b)

35
Q

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

A

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

36
Q

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

A

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

37
Q

how do you factor a polynomial with 4 terms

A

factor by grouping

38
Q

what is the remainder theorem

A

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

39
Q

what is the factor theorem

A

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

40
Q

what is the rational zero test

A

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

41
Q

how many real zeros does a function have

A

whatever its degree is

42
Q

how many relative max/min does a function have

A

degree-1

43
Q

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

A

^ ^
I I

|

44
Q

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

A

I ^
v I

45
Q

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

A

I I
V V

46
Q

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

A

^ I
I V

47
Q

what is the multiplicity of a zero

A

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

48
Q

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

A

pass through

49
Q

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

A

squiggle (cubic)

50
Q

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

A

bounce (parabola)

51
Q

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

A

a-sqrt b

Scholars Classes Flashcards (12 decks)

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