AFDA – Unit 4: Quadratic Functions
Day 1 Notes: Graphing Quadratics in Vertex Form
Name: _________________
Block: _____ Date:_______
Today you will be
 describing the behavior and characteristics of quadratic graphs
 graphing quadratics in vertex form
 writing an equation of a quadratic given a graph
Something old…
Domain – the ________________ or ______ values.
 Practical domain is the replacement x-values that makes sense in the context of
a real life situation.
 When looking at the graph, read __________________________ to
______________________ for the domain.
Range – the _________________ or ______ values.
 Practical range is the result of a function describing a real life situation.
 When looking at the graph, read __________________________ to
______________________ for range.
𝒚-intercept: the point(s) at which the graph crosses the 𝑦-axis (0, #)
Something new…
𝒙-intercept: the point(s) at which the graph crosses the 𝑥-axis. (#,0)
o quadratic roots/ roots
o zeros
o solutions
Parabola: U shaped curve created when graphing a quadratic function
Quadratics
Quadratic Parent Function:
𝑓(𝑥) = 𝑥 2
𝑥
𝑓(𝑥)
Direction:
AOS:
Vertex:
(Min or Max)
D:_______________R: ________________
Roots: __________ Y intercept: ________
Vertex Form
𝑓(𝑥) = 𝑎(𝑥 − ℎ)2 + 𝑘
Vertex: (ℎ, 𝑘)
**h is opposite sign
AoS: 𝑥 = ℎ
Same value as x in
vertex
Roots
Use calculator to
find “zeros”
y-intercept
Use calculator table
(0, #)
Using what you remember about a, h, and k shifts, describe the transformations
of the following equations.
1. 𝑦 = (𝑥 − 2)2
1
4. 𝑦 = (𝑥 + 1)2
2
2. 𝑦 = (𝑥 − 2)2 + 3
3. 𝑦 = −(𝑥 − 2)2 + 3
1
6. 𝑦 = 2(𝑥 − 3)2 − 1
5. 𝑦 = − 𝑥 2 + 1
4
7.
𝑓(𝑥) = (𝑥 + 3)2 + 4
𝑥
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
𝑓(𝑥)
(Min or Max)
Translations:
D:___________R: ____________
Zeros: ________________ Y int.: __________
8.
1
𝑓(𝑥) = (𝑥 − 2)2 − 3
2
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
𝑥
𝑓(𝑥)
(Min or Max)
Translations:
D:___________R: ____________
Solutions: ____________ Y int.: __________
9.
𝑓(𝑥) = −(𝑥 + 1)2
𝑥
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
𝑓(𝑥)
(Min or Max)
Translations:
D:___________R: ____________
X-int.: ____________ Y int.: __________
10. 𝑓(𝑥) = −𝑥 2 − 3
𝑥
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
𝑓(𝑥)
(Min or Max)
Translations:
D:___________R: ____________
Roots: ____________ Y int.: __________
Write the equation of each parabola in vertex form. Identify the requested information.
11.
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
(Min or Max)
Translations:
D:___________R: ____________
Zeros: ____________ Y int.: __________
12.
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
(Min or Max)
Translations:
D:___________R: ____________
Roots: ____________ Y int.: __________
13.
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
(Min or Max)
Translations:
D:___________R: ____________
Solutions: ____________ Y int.: ________
14.
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
(Min or Max)
Translations:
D:___________R: ____________
X-int.: ____________ Y int.: __________