Algebra

Question 1

DOTS

difference of two squares

Answer 1

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

Question 2

SODOTC

sum or difference of two cubes

Answer 2

a^3 _ b^3 = (a _ b) (a^2 _ ab + b^2)

SIGNS : SOAP
same, opposite, always positive

a^3 + b^3 = (a + b) (a^2 - ab + b^2)
a^3 - b^3 = (a - b) (a^2 + ab + b^2)

Question 3

completing the square

Answer 3

• x^2 and y^2 coeffiecent = 1
• divide coefficient of middle term by 2
• square answer
• add product as constant of equation

can be used in converting circles from general to standard form

Question 4

slope-intercept form

linear function

Answer 4

y=mx+b

degree of x is 1

m = slope
b = y-intercept

Question 5

general form

linear function

Answer 5

Ax + By + C = 0

degree of x is 1

Question 6

y-intercept (from general form)

linear function

Answer 6

b = -C / B

Question 7

slope of a line equation (from general/standard form)

linear function

Answer 7

slope = -A / B

Question 8

slope of a line equation

linear function

Answer 8

slope = change in y / change in x

slope = y2 - y1 / x2 - x1

Question 9

domain and range

linear function

Answer 9

domain = R
range = R

all real numbers

Question 10

point-slope formula

linear function

Answer 10

y - y1 = m(x - x1)

given point and slope
get m by using slope formula

Question 11

general form

rational function

Answer 11

f(x) = P(x) / Q(x)

contains variables in denominator

Question 12

domain

rational function

Answer 12

domain = {x|x ≠ 0}

all real nos. EXCEPT value that will make denominator = 0

Question 13

range

rational function

Answer 13

• interchange x and y in equation
• solve for y

Question 14

domain

odd root radical function

Answer 14

domain = R

all real numbers

Question 15

domain

even root radical function

Answer 15

• solve ( radicand ≥ 0 )

radicand should never be negative (imaginary number)

Question 16

standard form

quadratic function

Answer 16

y = ax^2 + bx + c

highest degree of x is 2

Question 17

x-coordinate of vertex (from standard form)

quadratic functions

Answer 17

x = -b / 2a

Question 18

y-coordinate of vertex (from x-coordinate of standard form)

quadratic functions

Answer 18

replace x in the equation with answer from x = -b / 2a

Question 19

y-coordinate of vertex (from standard form)

quadratic functions

Answer 19

k = 4ac - b^2 /
4a

Question 20

vertex form

quadratic function

Answer 20

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

given vertex of the parabola

Question 21

domain

quadratic function

Answer 21

domain = R

Question 22

range

quadratic function

Answer 22

R: {y|y _ k}
k : y-coordinate of vertex

if parabola opens UPWARD (+a), greater than or equal to
if parabola opens DOWNWARD (-a), less than or equal to

Question 23

circle standard form

conic sections

Answer 23

(x-h)^2 + (y-k)^2 = r^2

center : (h,k)
radius : r

Question 24

conic sections general form

Answer 24

Ax^2 + Cy^2 + Dx + Ey + F = 0

A : coefficient of x^2
C : coefficient of y^2
F : constant

Question 25

parabola shortcut | conic sections general form

Answer 25

A or C is squared (x^2 OR y^2) | only one of the variables is squared

Question 26

parabola standard form | conic sections opening up or down

Answer 26

(x-h)^2 = 4a (y-k) | only the x variable is being squared ## Footnote -4a : opening DOWN +4a : opening UP (visualize cartesian plane and y-axis)

Question 27

parabola standard form | conic sections opening left or right

Answer 27

(y-k)^2 = 4a (x-h) | only they variable is being squared ## Footnote -4a : opening LEFT +4a : opening RIGHT (visualize cartesian plane and x-axis)

Question 28

hyperbola shortcut | conic sections general form

Answer 28

A and C are squared different signs | multiplying A and C will give a negative product

Question 29

hyperbola standard form | horizontal transverse axis

Answer 29

[(x-h)^2 / a^2] - [(y-k)^2 / b^2] = 1 | x is first term

Question 30

hyperbola standard form | vertical transverse axis

Answer 30

[(y-k)^2 / a^2] - [(x-h)^2 / b^2] = 1 | y is first term

Question 31

circle shortcut | conic sections general form

Answer 31

A and C are squared A and C are equal | coefficients of x^2 and y^2 are equal

Question 32

ellipse shortcut | conic sections general form

Answer 32

A and C are squared same signs, but not equal | A and C are not the same number A x C will give positive product

Question 33

ellipse standard form | conic sections

Answer 33

[(x-h)^2 / a^2] + [(y-k)^2 / b^2] = 1 if b > a = vertical major axis | if a > b = horizontal major axis ## Footnote larger number is below X = HORIZONTAL larger number is below Y = VERTICAL

Question 34

center of a circle | general form ( if A and C = 1 )

Answer 34

h = -D / 2 k= -E / 2 r = -F + h^2 + k^2 ## Footnote D : coefficient of X E : coefficient of Y F : constant

Question 35

converting logarithm -> exponential form

Answer 35

BREIN | Base Raised to Equal Is Natira ## Footnote logbA = e -> b^e = A

Question 36

exponential solving shortcut

Answer 36

BEBE Form | B^e = B^e ## Footnote - make bases the same - equate exponents to each other

Question 37

rationalizing | denominator with radical

Answer 37

multiply conjugate of denominator | square root goal : DOTS cube root goal : SODOTC ## Footnote cube root conjugate : a^2 _ ab + b^2 - first sign is opposite of given sign