Algebra II: Chapter 3

what is rate of change?

how a quantity is changing in regards to another quantity (slope)

how do you find the rate of change when it is not constant?

by taking the average of an interval

what is average rate of change equal to?

the change in the value of the dependent variable divided by the change in the value of the independent variable over a given interval

what is the general form of a quadratic?

f(x) = ax² + bx + c where a doesn’t = 0

in ax² + bx + c, a=

quadratic term

in ax² + bx + c, b=

linear term

in ax² + bx + c, c=

constant term

the a value is known as the…

leading coefficient

what is the formula for the axis of symmetry?

-b/2a

what is the domain of every single quadratic function?

negative infinity to positive infinity

if the a value is positive, the graph will open what direction (and vice versa)?

up

if a > 0, it has a…

minimum

if a < 0, it has a…

maximum

quadratic equation

an equation that contains a quadratic expression

a quadratic function can have__ , __, __ roots (x int.)

1, 2, or no

steps to solving a quadratic:

1. rearrange terms so one side is =0

2. find axis of symmetry and vertex

3. make a table for more points

4. graph parabola and identity x. int

5. check solutions in original equation

what should you do if exact roots can’t be found?

state the consecutive integers between the roots’ location

to double check “nice” roots, use what tool?

the table (2nd, graph)

name the factoring techniques

1. GCF

2. Reverse FOIL (check GCF)

3. Difference of Squares

4. Factor by Grouping

what is needed for factoring with differences of squares?

subtraction and perfect squares

after grouping, if possible…

continue factoring

foiling is ____ of factoring

reverse

GCF stays where in your equation?

in front