Unit 4 Flashcards
Steps to Factoring Trinomials
- Multiply a and c
- Set a to be multiplied in top of diamond and b is sum on bottom
- Add these factors to the two binomials with original a value
- Reduce
Difference of Two Squares
Binomials seperated by subtraction
Solutions to Quadratics Other Names
Zeros, roots, or x-intercepts
Number of Solutions in Quadratics
2 - two x-intercepts
1 - one x-intercept and repeated rroots
0 - zero x-intercepts
Ways to Solve Quadratics
- Graphing
- Factoring
- Square roots
- Quadratic formula
- Completing the square
- Calculator
Steps to Solving Quadratics by Factoring
- Move all terms to one side and set equal to 0
- Factor
- Set each factor equal to zero and solve for each x-value
- Write answer as list of zeros
Radical
Any expression with a square root, cube root, etc.
First 20 Perfect Squares
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400
Quadratic Equation of Solving By Square Roots
ax^2+c=0
x^2=n
x+_√n
Steps to Solving Quadratics By Square Roots
- Isolate x^2
- Take the square root of both sides
- Simplify the radical and write as list of x
Imaginary Numbers
Defined when there is no real solution
Pure Imaginary Number
bi
b=real number
i=imaginary number
Steps to Simplifying Negative Square Roots
- Rewrite √-a as √-1*a
- Break a down if it is not a perfect square
- Simplify the radical, recalling that √-1=i
Powers of “i” Base Four Number System
i^1=i
1^2=-1
1^3=-i
1^4=1
Memorize “i”
i=√-1
i^2=-1
Complex Number
Expression that defines a real number and pure imaginary number that are not like terms and cannot be combined
Complex Conjugates
(a+bi)(a-bi)=a^2+b^2
“i” Can Not Be
In the denominator of a complex number
Dividing Complex Numbers when Denominator is Monomial
Multiply top and bottom by i
Bottom becomes i^2
Dividing Complex Numbers when Denominator is Binomial
Multiply top and bottom by th conjugate
Use array
Steps to Completing the Square
- Rewrite as ax^2+bx=c
- Divide both sides by ao it becomes x^2+bx=c
- Complete the square by taking half of b, squaring it, and adding to both sides of the equation
- Factor the perfect square trinomial
- Take the sqaure root of both sides, creating a positive and a negative case
- Solve both equations, simplifying all irrational and complex answers
Completing the Square
Taking a quadratic equation, creating a perfect square trinomial, and solving it in a similar way
Formula For The Discriminant of a Quadratic
d=b^2-4ac
Value of D and Roots
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
Choosing Best Method
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
Quadratic Word Problems
- Draw a picture
- 2nd, trace, max or zero
X is always independent
Quadratic Regression
Method to write curve of best fit
Curve of Best Fit
Data in a curve following a pattern
Steps to Quadratic Regression
- Hit stat, enter
- Enter x-values in L1 and y-values in L2
- Hit stat and arrow over to calc
- Choose 5-quadreg
- Hit enter possibly twice
Vertex Form
y=(h-k)^2+k
h=axis of symmetry
k=y-value in vertex
Finding Axis of Symmetry
x=b/2
Factored Form
(x+p)(x+q)
Standard Form From Vertex Form
Multiply in array and add
Solving By Square Roots With Parenthesis Squared
Just find square root of both sides after isolating parenthesis
