Quadratic Equations and Graphical Analysis

Foil method

Foil Shortcuts

Quadratic Formula

What is the product of the roots?

c/a

What is the sum of the roots

-b /a

what is the discriminant and how does it help us

• b² - 4ac

• Helps us to quickly determine the number of solutions a quadratic equation has

  • Greater than 0 = 2 solutions

  • = 0 means 1 solution

  • Less than zero or negative = 0 solutions

factoring trinomials with x²

what factors of c will add up to b

factoring trinomials with ax²

what factors of a*c will add up to b; write out answers as b and factor out answer

X² - Perfect square

(x+srt) (x-srt)

how to find perpendicular line slope if given original line slope

take the negative reciprocal

parallel lines have

the same slope

2 point formula for the slope of a line

m= (y2 - y1) / (x2 - x1)

how to find vertex of a quadratic

x of vertex = -b/2a; then plug in answer into quadratic to find y

Cubic function

• has defining squiggle

  

absolute value functions

A like shape that forms something that likes a right angle

Square root function

distance formula