Unit 5: Quadratic Functions Algebra II with Trigonometry
Unit 5:
Quadratic Functions
LESSON #4:
VERTEX FORM
OF A
PARABOLA
Recall: Quadratic Functions
Quadratic Functions
An equation in the form , where 0 is a quadratic function expressed in vertex form of a parabola.
VertexFormisa
seriesoftransformations
oftheparentfunction
Recall:H S R V
*Note: Quadratics in the form of where
0 are not functions. Lesson #4 Vertex Form of A Parabola
, 1
Unit 5: Quadratic Functions Algebra II with Trigonometry
Properties of a Parabola
VertexFormofaParabola

AxisofSymmetry:
Formula:



Vertex:
Formula:
,
,
*Note: The ‐value in the function is “opposite” of what it looks like and the ‐value “is what it is”. Ex) Vertex: ,
TRANSFORMATION PROPERTIES
Lesson #4 Vertex Form of A Parabola
2
Unit 5: Quadratic Functions Algebra II with Trigonometry
Ex 1) Sketch the graph and identify the given information:
Axis of Symmetry:
,
Vertex:
Max? or Min?: Max
,
y‐intercept:
H: Right 1
S: NONE
R: Reflection over
x-axis
V: Up 4
Ex 2) Sketch the graph and identify the given information:
Axis of Symmetry:
Vertex:
,
Max? or Min?:
y‐intercept:
Min
,
H: Left 2
S: Vertical Shrink by
factor
*multiply
‐valuesby *
R: NONE
V: Down 3
Lesson #4 Vertex Form of A Parabola
3
Unit 5: Quadratic Functions Algebra II with Trigonometry
Ex 3) Write the equation of the parabola in vertex form.
-3
a = _____
2
h = _____
k = _____
6
Ex 4) Write the equation of the parabola in vertex form.
a = _____
-3
h = _____
-1
k = _____
Lesson #4 Vertex Form of A Parabola
4
Unit 5: Quadratic Functions Algebra II with Trigonometry
How can we transform
standard form to vertex form?
Use the process of completing the square!
Goal:
Given:
Standard Form
Vertex Form
Ex 1) Re-write
vertex form.
Steps:
Move
in
Goal:
Step 1:
value.
Step 2:
Factor
value.
[NOTthe !]
Step 3:
Complete the
square on the
expression inside
the parentheses.
Lesson #4 Vertex Form of A Parabola
5
Unit 5: Quadratic Functions Algebra II with Trigonometry
Steps:
Ex 1) Re-write
vertex form.
in
Step 4:
Value of
must be multiplied
by -value before
added to
side.
Step 5:
Factor the perfect
square trinomial.
Step 6:
Move
value back
to the other side.
Ex 2) Re-write
in vertex form.
Identify and classify the vertex as a max or min.
13
VERTEX: (2,‐13)
Minimum
Lesson #4 Vertex Form of A Parabola
6
Unit 5: Quadratic Functions Algebra II with Trigonometry
Ex 3) Re-write
in vertex form.
Identify and classify the vertex as a max or min.
23
4
VERTEX:
,
Minimum
Lesson #4 Vertex Form of A Parabola
7