Quadratic Relations
By Nana Sarpong
Quadratic 1: Graphed Quadratic Relationship
Key features of Quadratic Relations
Step Pattern and Possible Value of for X and Y
Step Pattern
A parabolas without "A" in it's equation, step pattern will always be over 1, up 1 and over 2, up 4
Equation Forms of Quadratic and graphing
Vertex Form
H equal to the xaxis of the vertex and the axis of symmetry
K equal to the yaxis of the vertex and the Optimal Value.
A multiples the yaxis in step pattern and if A is negative, the parabolas will open downwards and if A is positive, the parabolas will open upwards
Standard or Trinomial Form
C is the same as yintercept
A multiples the yaxis in step pattern and if A is negative, the parabolas will open downwards and if A is positive, the parabolas will open upwards
Binomials or factored Form
H & K are the 2 xintercepts
X equal to the xaxis of the vertex and the axis of symmetry
Y equal to the yaxis of the vertex and the Optimal Value
A value only change the Optimal Value
Linear and Quadratic Relationship
 Linear Relationships have equal 1st differences
 Quadratic Relationships have equal 2nd differences
Quadratic 2: Expanding and factoring Quadratic Expression
Multiplying Common Binomials or changing factored form to standard form
Building Blocks
 Rainbow way
 Binomial Common Factoring

Building Blocks
 when 2 Xs meet they make x^2
 when x and 1 meet they make 1x
 when 1 and 1 meet they make 1
Rainbow way
 times both Xs to get X^2
 times x and 3 to get 3X
 times x and 2 to get 2X
 times 3 and 2 to get 6
 then add 3X and 2X to get 5X
Factoring by Grouping
In order to factor binomial with 4 terms you must factor it in pairs
AX+BX+CX+DX take the 1st 2 terms and factor them
 do the same with the 3rd and 4th terms
Factoring Simple Trinomials or changing standard form to factored form
Simple are Trinomials with a coff of 1.
Ex.X+BX+C
To factor trinomials you must remember this rulesX is always X^2
C is equal to two of it's factors
B is the sum of C's factors
see Picture for Examples
Factoring Complex Trinomials
Ex.AX+BX+C
To factor this you must change to a simple Trinomial by find the GCF of A, B, and C
If there is no GCF than use the Trial and Error to find answer
see Picture for Examples
Factoring Perfect Squares
(XR)^2=(XS)(XR)
To factor this you could factor as if it was common binomials or
1. squares X.
2. times X and R together than times by 2.
3. Squares R.
see Picture for Examples
Factoring Difference of squares
X^2R=(XR)(X+R)
To factor this is
1. find square root of X and R.
2. then to it together one negative and one positive
See Picture for Example
Quadratics Part 3: Solving Quadratic Equation
Solving Quadratic equations by factoring or Finding Xintercepts from standard form
 always sub:Y=0
 factor the equation
 isolate X
 solve by Elimination
 Check for work
Completing the square or changing standard form(AX^2+BX+C) to vertex form(A(XB)^2+C)
 divide B by A then take x^2+bx in a bracket and leave c alone = y=A(X^2+BX)+C
 divide b by 2 then square it by 2 = (B/2)^2
 put the total with x^2+bx = A(X^2+B+D)+C
 subtract or add D to rid of it = A(X^2+B+D+/F)+C
 factor X^2+B+D then times A with F and then take the total out of the bracket = A(X+B)^2+/F+C
 add or subtract F and C = A(XB)^2+C
Finding the zeros/roots/xintercepts from Vertex Form
Solving Quadratic Equation with the Quadratic Formula
Examples below