Algebra Ii: Quadratic Equations

Front 1

standard form

Back 1

y = ax^2 + bx + c

Front 2

quadratic term

Back 2

ax^2 - to the 2nd degree

Front 3

linear term

Back 3

bx - to the 1st degree

Front 4

constant

Back 4

c - no variables

Front 5

vertex form

Back 5

a(x-h)^2 + k

Front 6

parabola

Back 6

graph of quadratic equations

Front 7

vertex (in terms of graph)

Back 7

(LOS, min/max y-value)

Front 8

vertex (in terms of vertex form)

Back 8

(h, k)

Front 9

factoring

Back 9

finding an equivalent expression to an expression that is a product of expressions

Front 10

scaler factoring

Back 10

combine common term factors among terms and group other term factors

e.g. ax^2 + bx → x(ax + b)

Front 11

greatest common factor

Back 11

the product of scaler factoring

Front 12

prime solution

Back 12

solution is not factorable

Front 13

perfect square trinomial

Back 13

equal binomials squared

A^2 + 2AB + B^2 = ?

Hint 13

(A+B)^2

Front 14

difference of squares

Back 14

A^2 - B^2 = ?

Hint 14

(A+B)(A-B)

Front 15

zero product rule

Back 15

AB = 0

Front 16

sum of cubes

Back 16

(A+B)(A^2 - AB + B^2) = ?

Hint 16

A^3 + B^3

Front 17

difference of cubes

Back 17

(A-B)(A^2 + AB + B^2) = ?

Hint 17

A^3 - B^3

Front 18

primary and secondary root

Back 18

primary = positive root from solution of radical
secondary = negative root from solution of radical

Front 19

multiplication property of radicals

Back 19

√(ab) = √a √b

Front 20

If the index is higher than the exponents of your radicand (as long as powers are prime), the solution is _?

e.g. ^4√(5^3)

Back 20

simplified

Front 21

addition of like radicals

Back 21

a√x + b√x = (a+b)√x

Front 22

quotient rule for radicals

Back 22

√(a/b) = √a / √b

Front 23

A fractional radicand or radical denominator is _?

Back 23

improper

Front 24

x^-a = ?

Back 24

1 / x^a

Hint 24

Move the term to the bottom and make it positive.

Front 25

1 / x^-a = ?

Back 25

x^a

Hint 25

Move the term to the top and make it positive.

Front 26

conjugates

Back 26

writing the sum of two terms as difference or writing the difference of two terms as a sum

e.g. √a + √b = conjugate of √a - √b

Front 27

imaginary unit

Back 27

i

Front 28

(imaginary #)(imaginary #) = ?

Back 28

real number

√-9 x √-16 = √144 = 12

Front 29

complex numbers

Back 29

have real and imaginary parts

A + Bi

Front 30

1) i^1 = ?
2) i^2 = ?
3) i^3 = ?
4) i^4 = ?

Back 30

1) i
2) -1
3) -i
4) 1

Front 31

square root property

Back 31

take square root of both sides of equation after squared variable is isolated

Front 32

A^2 - 2AB + B^2 = ?

Back 32

(A-B)^2

Front 33

4 methods to solve quadratic equations

Back 33

1) table of values
2) factoring
3) completing the square
4) quadratic formula

Front 34

quadratic formula

Back 34

x = (-b +/- √(b^2-4ac))/2a

Front 35

discriminant

Back 35

b^2 - 4ac

Front 36

1) discriminant < 0
2) discriminant = 0
3) discriminant > 0

Back 36

1) no real roots
2) 1 real root
3) 2 real roots

Front 37

using a to find two extra points

Back 37

(x +/- 1, y + a)