A.
Name: _____________________________________________
(when given their graph)
B.
General Form: A. _____________________ B. _______________________
Vertex:
Function: (use a

1 )
A. _____________________ B. _______________________
A. _____________________ B. _______________________
Range: A. _____________________ B. _______________________
Domain: A. _____________________ B. _______________________ x -intercepts (aka. “ roots ” “ zeros ”): A. _____________________ B. _______________________ y -intercept:
Interval of increase:
Interval of decrease
A. _____________________ B. _______________________
A. _____________________ B. _______________________
A. _____________________ B. _______________________ f (2) 7 ( 5) : A. _____________________ B. _______________________
Could nearly all of these “features” be studied on a higher order polynomial like the one pictured to the right??
__________________________

1. What is the vertex of each function below? What is the equivalent function written in vertex form? a . f x
 
3 x
2 
6 x

2 b.
g x

2 x
2 
4 x

5
Equivalent Vertex Form:
______________________________
Equivalent Vertex Form:
______________________________
The key to finding the interval of increase or the interval of decrease is to know the _______________.
2. What is the interval of increase and the interval of decrease for each function listed below? a . f x

2 x
2 
12 x

3 b.
( )
 
3
 x

7

2 
2
Increasing: ____________________ Increasing: ____________________
Decreasing: ____________________ c. ( )
  x
  x

2

Decreasing: ____________________
Decreasing: ____________________
Increasing: ____________________

To find the x-intercepts of a function___________________________ and solve the resulting equation.
To find the y-intercept___________________________________ and simplify.
3. What is the x -intercept and y -intercept of each function below? a . ( )
 x
2 
13 x

36 b.
m x
 x
2 
7 x xintercepts : ____________________ xintercepts : ____________________ yintercept : ____________________ yintercept : ____________________ c . k x

3 x
2 
7 x

6 xintercepts : ____________________ d.
( )
 
3 x

5
 x

2

xintercepts : ____________________ yintercept : ____________________ yintercept : ____________________
Lastly, two synonyms for “x-intercepts” are ____________________and _______________________.

A quadratic function can have 2 real roots , one real root , or two imaginary roots .
4. Draw a rough sketch of each scenario listed above.
Two Real Roots One Real Root Two Imaginary Roots
5. Determine how many x -intercepts each function has. a. f x
 x
2 
4 x

45 b. ( )
 x
2 
12 x

36 c. h x
 x
2 
8 x

19 d. ( )
 
3 x
  x

2


6. What is the vertex of each absolute value function? What are the four transformations of each absolute value function? Lastly, write a quadratic function that has the same transformations. a . ( )
 
3 x 4 2
Vertex :
* b .

1
2 x 4 7
Vertex:
*
* *
* *
* *
Quadratic function with same transformations:
__________________________
7. Graph each absolute value function from above.
( )
 
3 x 4 2
Quadratic function with same transformations:
__________________________

1
4 7
2 x

8. What is the vertex of each function below? Name three additional points that are on its graph. a . ( )

3
 x

2

2 
4 b.
( )
 
2
 x

5

2 
3
9. What is the equation of each parabola described below? a . vertex of
  and goes through the point

5, 4

. b . vertex of

2, 5
 and goes through the point

0, 7

.
Final Answer:
Final Answer:

There are two ways to determine if a relation represents a function. They are:
A. ____________________________________ B. ________________________________________
10. Determine if each relation below represents a function. If it does not, state why it doesn’t. a .
            
_______________________________________________ b .
        
6, 5
 
_______________________________________________ c. d. e.
________________________
________________________
________________________
________________________
________________________
________________________
Reflect:
Which questions are the easiest for you? ____________________________________________
____________________________________________________________________________
Which questions are the most challenging ? __________________________________________
____________________________________________________________________________

1. What is the equation of the parabola that has a vertex of

5, 7

and goes through the point

3,

39

?
2. What is the vertex form of g x
 x
2 
8 x

9 ?
3. What are the roots of f x

3 x
2 
10 x

8 ? 4. What are the zeros of ( )

2 x
2  
10 ?
5. Describe the transformations of each function listed below:
a. ( ) x 5 6 b. ( )
 
2
 x

3

2 
7