Analytic Geometry Unit 5 Quadratic Functions
Name:
QUADRATIC FUNCTION FORMS
MCC9-12.F.IF.8
Write a quadratic function defined by an expression in different but equivalent
forms to reveal and explain different properties of the function.
EQ: How should we write and graph a quadratic function of the forms f(x) = ax2 + bx + c (standard form)
and f(x) = a(xh)2 + k (vertex form) to reveal and explain different properties of the function?
CONVERTING QUADRATIC EQUATIONS FROM STANDARD FORM INTO VERTEX FORM
TO

(Standard Form)
f(x) = ax2 + bx + c
Step 1
Step 2
How should
we identify
a, b and c?
How should we
find the
axis of symmetry
xh
b
?
2a
(Vertex Form)
a(xh)2 + k
Step 3
Step 4
How should we
find f(h)?
How should
we rewrite f(x)
in
vertex form?
Step 5
On a grid, how do we graph
the axis of symmetry and the
function and identify the
vertex as a maximum or
minimum?
For #1-3, how should we write the quadratic function f(x) from standard to vertex form and graph f(x)?

Step 1
Step 2
Step 3
Step 4
Step 5
f(x) = -2x2 + 12x  13

1
2
f(x) = - x2 + 4x  7

f(x) = -2x2 + 4x +1
Analytic Geometry Unit 5 Quadratic Functions
Name:
QUADRATIC FUNCTION FORMS
Write a quadratic function defined by an expression in different but equivalent
forms to reveal and explain different properties of the function.
MCC9-12.F.IF.8
EQ: How should we write and graph a quadratic function of the forms f(x) = ax2 + bx + c (standard form)
and f(x) = a(xh)2 + k (vertex form) to reveal and explain different properties of the function?
CONVERTING QUADRATIC EQUATIONS FROM STANDARD FORM INTO VERTEX FORM
TO

(Standard Form)
2
f(x) = ax + bx + c
Step 1
Step 2
How should
we identify
a, b and c?
How should we
find the
axis of symmetry
xh
b
?
2a
(Vertex Form)
a(xh)2 + k
Step 3
Step 4
How should we
find f(h)?
How should
we rewrite f(x)
in
vertex form?
Step 5
On a grid, how do we graph
the axis of symmetry and the
function and identify the
vertex as a maximum or
minimum?
For #4-6, how should we write the quadratic function f(x) from standard to vertex form and graph f(x)?

Step 1
Step 2
Step 3
Step 4
Step 5
1
2
f(x) = - x2  2x +1

f(x) = 2x2  12x + 17

f(x) =
1
2
x2  2x  3
Analytic Geometry Unit 5 Quadratic Functions
Name:
QUADRATIC FUNCTION FORMS
Write a quadratic function defined by an expression in different but equivalent
forms to reveal and explain different properties of the function.
MCC9-12.F.IF.8
EQ: How should we write and graph a quadratic function of the forms f(x) = ax2 + bx + c (standard form)
and f(x) = a(xh)2 + k (vertex form) to reveal and explain different properties of the function?
CONVERTING QUADRATIC EQUATIONS FROM VERTEX FORM INTO STANDARD FORM
TO

(Vertex Form)
2
a(xh) + k
Step 1
Step 2
On the graph, how
should we identify the
axis of symmetry,
vertex and rate of
change?
How should we write
the equation of the
graph in vertex form?
(Standard Form)
f(x) = ax2 + bx + c
Step 3
Step 4
Step 5
How should we write
the binomial square as
two binomials?
How should we
expand the binomial
square into a trinomial
using FOIL?
How should we
combine like terms to
obtain standard form?
For #7-9, how should we write the graph of the quadratic function f(x) from vertex to standard form?
7
Step 1
Step 2
Step 3
Step 4
Step 5
8
9
Analytic Geometry Unit 5 Quadratic Functions
Name:
QUADRATIC FUNCTION FORMS
Write a quadratic function defined by an expression in different but equivalent
forms to reveal and explain different properties of the function.
MCC9-12.F.IF.8
EQ: How should we write and graph a quadratic function of the forms f(x) = ax2 + bx + c (standard form)
and f(x) = a(xh)2 + k (vertex form) to reveal and explain different properties of the function?
CONVERTING QUADRATIC EQUATIONS FROM VERTEX FORM INTO STANDARD FORM
TO

(Vertex Form)
2
a(xh) + k
Step 1
Step 2
On the graph, how
should we identify the
axis of symmetry,
vertex and rate of
change?
How should we write
the equation of the
graph in vertex form?
(Standard Form)
f(x) = ax2 + bx + c
Step 3
Step 4
Step 5
How should we write
the binomial square as
two binomials?
How should we
expand the binomial
square into a trinomial
using FOIL?
How should we
combine like terms to
obtain standard form?
For #10-12, how should we write the graph of the quadratic function f(x) from vertex to standard form?
10
Step 1
Step 2
Step 3
Step 4
Step 5
11
12
Analytic Geometry Unit 5 Quadratic Functions
Name:
QUADRATIC FUNCTION FORMS
MCC9-12.F.IF.8
Write a quadratic function defined by an expression in different but equivalent
forms to reveal and explain different properties of the function.
EQ: How should we write and graph a quadratic function of the forms f(x) = ax2 + bx + c (standard form)
and f(x) = a(xh)2 + k (vertex form) to reveal and explain different properties of the function?
For #13-16, the absolute value of the rate of change for the quadratic function is
1
2
. How should we write
a quadratic function in vertex form and standard form that satisfy the given properties?
PROPERTIES
13 The quadratic function f(x) has these
characteristics:
 The vertex is located at ( 8, -2 ).
 The range is -2  y  .
14 The quadratic function f(x) has these
characteristics:
 The axis of symmetry is x = -6.
 The range is -  y  4.
15 The quadratic function f(x) has these
characteristics:
 The vertex is located at ( 4, -1 ).
 The range is -  y  -1.
16 The quadratic function f(x) has these
characteristics:
 The axis of symmetry is x = 2.
 The range is 3  y  .
VERTEX FORM
STANDARD FORM
Analytic Geometry Unit 5 Quadratic Functions
Name:
QUADRATIC FUNCTION FORMS
MCC9-12.F.IF.8
Write a quadratic function defined by an expression in different but equivalent
forms to reveal and explain different properties of the function.
EQ: How should we write and graph a quadratic function of the forms f(x) = ax2 + bx + c (standard form)
and f(x) = a(xh)2 + k (vertex form) to reveal and explain different properties of the function?
For #17-20, the absolute value of the rate of change for the quadratic function is 2. How should we write
a quadratic function in vertex form and standard form that satisfy the given properties?
CHARACTERISTICS
17 The quadratic function f(x) has these
characteristics:
 The vertex is located at ( 4, -5 ).
 The range is -5  y  .
18 The quadratic function f(x) has these
characteristics:
 The axis of symmetry is x = 8.
 The range is -  y  -5.
19 The quadratic function f(x) has these
characteristics:
 The vertex is located at ( 6, -3 ).
 The range is -  y  -3.
20 The quadratic function f(x) has these
characteristics:
 The axis of symmetry is x = -2.
 The range is 4  y  .
VERTEX FORM
STANDARD FORM