Advanced Math
Quadratics [Day 3]
Notes: Converting from General to Vertex Form
Name:___________________________
2016
WARM UP : Think back to the procedure for completing the square in order to complete the blanks.
a.
b.
c.
Use your notes from D1 and D2 to fill in the following information:
Quadratic Function in GENERAL FORM
Quadratic Function in VERTEX FORM
How to find the vertex in GENERAL FORM
How to find the vertex in VERTEX FORM
**Notice**
_______ is the one thing that doesn’t change in both forms!
To convert an equation from general to vertex form, __________________________________________
When
: Use the method of completing the square to find the vertex form of the quadratic function.
Identify the vertex and axis of symmetry. Does the quadratic have a max or a min? What is the max or min?
Lastly, identify the domain and range (in interval notation).
Example 1:
vertex form:_________________________ vertex:____________________
axis of symmetry:_________
max or min:____________
domain: ________________
range:__________________
When
: Use the method of completing the square to find the vertex form of the quadratic function.
Identify the vertex and axis of symmetry. Does the quadratic have a max or a min? What is the max or min?
Lastly, identify the domain and range (in interval notation).
Example 2:
vertex form:_________________________ vertex:____________________
axis of symmetry:_________
max or min:____________
domain: ________________
range:__________________
When
: Use
to find the -coordinate of the vertex. Then plug that value back into the
equation to find the -coordinate of the vertex. What you have found is ______________!! Lastly, identify
the value for , and put the equation into vertex form.
Example 3:
What is the value for ?
What is the value for ?
What is the value for ?
Take those values and put them into the equation
How does it open?
:________________________________
axis of symmetry:_________ max or min:____________ domain: ______________ range:____________
Example 4:
a.
Using the procedure from Example 3, write the equation in vertex form.
b.
Advanced Math
Quadratics [Day 3]
HW: Converting from General to Vertex Form
Name:___________________________
2016
When
: Use the method of completing the square to find the vertex form of the quadratic function. Identify the
vertex and axis of symmetry. Does the quadratic have a max or a min? What is the max or min? Lastly, identify the
domain and range (in interval notation).
1.
vertex form:_________________________
vertex:____________________
axis of symmetry:___________
max or min:______________
domain: ___________________
range:_____________________
2.
vertex form:_________________________
vertex:____________________
axis of symmetry:___________
max or min:______________
domain: __________________
range:____________________
3.
vertex form:_________________________
vertex:____________________
axis of symmetry:___________
max or min:______________
domain: __________________
range:____________________
4.
vertex form:_________________________
vertex:____________________
axis of symmetry:___________
max or min:______________
domain: __________________
range:____________________
When
: Use
to find the -coordinate of the vertex. Then plug that value back into the
equation to find the -coordinate of the vertex. What you have found is
. Lastly, identify the value for
, and put the equation into vertex form. For #5 and #6, also find the axis of symmetry, max/min, domain
and range.
5.
vertex:__________________
___________
opens:______________
vertex form:______________________________
axis of sym:__________
max or min:______________
domain: __________________
range:____________________
6.
vertex:__________________
___________
opens:______________
vertex form:______________________________
axis of sym:__________
max or min:______________
domain: __________________
range:____________________
7.
vertex:__________________
___________
opens:______________
vertex form:______________________________
8.
vertex:__________________
___________
opens:______________
vertex form:______________________________
; vertex:
; axis of symmetry:
2.
; vertex:
; axis of symmetry:
3.
; vertex:
; axis of symmetry:
; min value:
; domain:
; range: [
4.
; vertex:
; axis of symmetry:
; min value:
; domain:
; range: [
; axis of symmetry:
; max value:
5.
6.
7.
; vertex:
; vertex:
; vertex:
; axis of symmetry:
; min value:
; range: [
1.
; min value:
; min value:
8.
; domain:
; range: [
; domain:
; domain:
; range:
; range: [
; domain:
; vertex:
]