Getting Started Chapter 1 Flashcards
Square of sum
(a+b)=a^2+2ab+b^2
(a-b)=a^2-2ab+b^2
Ways to factor and expression
- square of sum
- decomposition
- expand the square
How to expand the square
- Expand the bracket
- Set up the distribution for the bracket
- Distribute
- Combined like terms
f(x)+d
verticle translation up d units
f(x)-d
verticle translation down d units
f(x+c)
horizontal translation left c units
f(x-c)
horizontal translation right c units
-f(x)
reflection over x-axis
f(-x)
reflection over y-axis
af(x)
verticle stretch when a is greater than 1
verticle compression when a is between 1 and 0
f(bx)
horizontal compression when b is greater than 1
horizontal stretch when b is between 1 and 0
what is the square of sum
use the formula (a+b)^2=a^2 + 2ab + b^2
square root the first and last numbers
plug those two numbers in the bracket
use the original formula to see if the bracket is correct
by using the last number in the bracket to see if the second number in the formula is that number squared times two
then see if the third number in that formula is that number squared
what is expanding that square
write the formula again but expand that square
isolate the first variable from the first bracket
isolate the second variable from the second bracket
rewrite the distributed form
combine like terms
how to state the domain and range of a graph
state the start and finish of the x-axis in an interval
state the start and finish of the y-axis in an interval
how to state the domain and range of a function
Finding domain:
look at the value “a” to identify if the graph will open upwards or downwards
Finding Range:
use k=-b^2-4ac/4a to find the k value, the k value is the maximum or minimum point of the graph
use the answer to write the range in notation form example if 0 is the answer, the notation form would be {y|y>=0}
