Unit 4

Question 1

Steps to Factoring Trinomials

Answer 1

1. Multiply a and c
2. Set a to be multiplied in top of diamond and b is sum on bottom
3. Add these factors to the two binomials with original a value
4. Reduce

Question 2

Difference of Two Squares

Answer 2

Binomials seperated by subtraction

Question 3

Solutions to Quadratics Other Names

Answer 3

Zeros, roots, or x-intercepts

Question 4

Number of Solutions in Quadratics

Answer 4

2 - two x-intercepts
1 - one x-intercept and repeated rroots
0 - zero x-intercepts

Question 5

Ways to Solve Quadratics

Answer 5

1. Graphing
2. Factoring
3. Square roots
4. Quadratic formula
5. Completing the square
6. Calculator

Question 6

Steps to Solving Quadratics by Factoring

Answer 6

1. Move all terms to one side and set equal to 0
2. Factor
3. Set each factor equal to zero and solve for each x-value
4. Write answer as list of zeros

Question 7

Radical

Answer 7

Any expression with a square root, cube root, etc.

Question 8

First 20 Perfect Squares

Answer 8

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400

Question 9

Quadratic Equation of Solving By Square Roots

Answer 9

ax^2+c=0

Question 10

x^2=n

Answer 10

x+_√n

Question 11

Steps to Solving Quadratics By Square Roots

Answer 11

1. Isolate x^2
2. Take the square root of both sides
3. Simplify the radical and write as list of x

Question 12

Imaginary Numbers

Answer 12

Defined when there is no real solution

Question 13

Pure Imaginary Number

Answer 13

bi
b=real number
i=imaginary number

Question 14

Steps to Simplifying Negative Square Roots

Answer 14

1. Rewrite √-a as √-1*a
2. Break a down if it is not a perfect square
3. Simplify the radical, recalling that √-1=i

Question 15

Powers of “i” Base Four Number System

Answer 15

i^1=i
1^2=-1
1^3=-i
1^4=1

Question 16

Memorize “i”

Answer 16

i=√-1
i^2=-1

Question 17

Complex Number

Answer 17

Expression that defines a real number and pure imaginary number that are not like terms and cannot be combined

Question 18

Complex Conjugates

Answer 18

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

Question 19

“i” Can Not Be

Answer 19

In the denominator of a complex number

Question 20

Dividing Complex Numbers when Denominator is Monomial

Answer 20

Multiply top and bottom by i
Bottom becomes i^2

Question 21

Dividing Complex Numbers when Denominator is Binomial

Answer 21

Multiply top and bottom by th conjugate
Use array

Question 22

Steps to Completing the Square

Answer 22

1. Rewrite as ax^2+bx=c
2. Divide both sides by ao it becomes x^2+bx=c
3. Complete the square by taking half of b, squaring it, and adding to both sides of the equation
4. Factor the perfect square trinomial
5. Take the sqaure root of both sides, creating a positive and a negative case
6. Solve both equations, simplifying all irrational and complex answers

Question 23

Completing the Square

Answer 23

Taking a quadratic equation, creating a perfect square trinomial, and solving it in a similar way

Question 24

Formula For The Discriminant of a Quadratic

Answer 24

d=b^2-4ac

Question 25

Value of D and Roots

Answer 25

d>0 perfect square - 2 real, rational roots
d>0 not perfect square - 2 real, irrational roots
d=0 - 1 real, rational root
d<0 - 2 imaginary roots

Question 26

Choosing Best Method

Answer 26

Graphing - roots are integers
Factoring - roots are rational
Square roots - no b-term
Completing the square - always, no coefficient and even b term
Quadratic formula - always

Question 27

Quadratic Word Problems

Answer 27

1. Draw a picture
2. 2nd, trace, max or zero
   X is always independent

Question 28

Quadratic Regression

Answer 28

Method to write curve of best fit

Question 29

Curve of Best Fit

Answer 29

Data in a curve following a pattern

Question 30

Steps to Quadratic Regression

Answer 30

1. Hit stat, enter
2. Enter x-values in L1 and y-values in L2
3. Hit stat and arrow over to calc
4. Choose 5-quadreg
5. Hit enter possibly twice

Question 31

Vertex Form

Answer 31

y=(h-k)^2+k
h=axis of symmetry
k=y-value in vertex

Question 32

Finding Axis of Symmetry

Answer 32

x=b/2

Question 33

Factored Form

Answer 33

(x+p)(x+q)

Question 34

Standard Form From Vertex Form

Answer 34

Multiply in array and add

Question 35

Solving By Square Roots With Parenthesis Squared

Answer 35

Just find square root of both sides after isolating parenthesis