Quadratics

Factoring

Common Factors

Find The Greatest Common Factor

30x^2 + 5y^2 + 15xy
= 5(6x^2 + y^2 + 3xy)
GCF = 5

Difference of Squares

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

Factor Quadratic Expressions

ax^2 + bx + c

a(x - r) (x - s)

Product - Sum Method

x^2 - 8x + 15
P: 15 = (-3 x -5)
S: -8 = (-3 + -5)
= (x-3) (x-5)

Used to find roots and factor

Perfect Square Trinomial

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

(x+6)^2= x^2 + 12x + 36

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

(x-2)^2 = x^2 - 4x + 4

Simplifying

1. Clear the Brackets

2. Collect Like Terms

3. Place from highest degree to lowest

Domain and Range

Domain: Set of all real values of x

Step Pattern

Step Pattern: a value multiplied
(1,3,5)
a = 5x
(1x5)=5
(3x5)=15
(5x5)=25
Therefore step pattern is (5,15,25)

Vertex Form:
y=a(x-h)^2+k
a = Stretch Factor
(h,k) = Vertex

X-Intercept Form
y= a(x+r)(x-s)
a = stretch factor
r = x - intercept
s = x - intercept

y= a(x+r) (x-s)

X-Intercept to Standard Form

Simplify (FOIL Method)

Standard form:
y = ax^2 +bx+c
c = y - intercept
a, b and c are parameters

Standard Form to X-Intercept Form

Product - Sum Method

Standard from to Vertex Form

Completing The Square

y= 5x^2 + 10x + 1
y = 5(x^2+2x)+1
y= 5(x^2+2x+1)+1 - 1(5)
y = 5 (x+1)^2 - 4

Quadratic Formula

Used to find the two roots of parabola