Pre-AP Algebra 2
Unit 3 – Lesson 4 – Converting Standard Form to Vertex Form
Objectives: The students will be able to
Convert from standard form to vertex form by completing the square
Factor with any value as a in
Materials: Do Now worksheet; pairwork; hw #3-4
Time
Activity
5 min
Review Homework
Show the answers to hw #3-3 on the overhead. Students correct their answers. Pass around the tally
sheets.
10 min
Homework Presentations
Review the top 2 or 3 problems.
15 min
Do Now
Hand out the Perfect Square Trinomials worksheet to students to complete. Review answers on the
overhead.
30 min
Direct Instruction
Background:
Perfect Square Trinomials Patterns:
(a + b)
2
= (a + b)(a + b) = a
2
+ 2ab + b
2
(a – b)
2
= (a – b)(a – b) = a
2
– 2ab + b
2
(x + 5)
2
= x
2
+ 2(5)(x) + 5
2
= x
2
+ 10x + 25
(3x – 4)
2
= (3x)
2
– 2(3x)(4) + 4
2
= 9x
2
– 24x + 16
Concepts:
Completing the Square: x
2
+ bx + c
To “complete the square” means to convert a standard form quadratic expression into a Perfect Square
Trinomial.
1) “Add and subtract” a number to make c = (b/2)
2
.
2) Factor the trinomial into (x + b/2)
2
3) If you are solving, work backwards from there.
Examples:
Convert each standard form parabola into vertex form by completing the square:
1) y = x
2
+ 6x
2) y = x
2
– 8x
3) y = x
2
+ 3x
4) y = x
2
+ 10x – 3
Completing the Square: ax
2
+ bx + c
When a is not 1:
1) Factor out a from first two terms – even if it’s not a factor.
2) Add (b/2)
2
, inside the parentheses.
3) Subtract a(b/2)
2
outside the parentheses. Don’t forget to multiply by a!
4) Factor the trinomial into a(x + b/2)
2
and simplify c
Example.
Convert into vertex form by completing the square:
5)
20 min
Pairwork
Pre-AP Algebra 2 Name: _______________________
Lesson #3-4: Do Now
Perfect Square Trinomials
1) Expand out each of the following. Remember, (a + b)
2
IS NOT a
2
+ b
2
.
a. (x + 5)
2
=
b. (x – 10)
2
=
c. (7 – x)
2
=
d. (2x + 3)
2
=
e. (a + b)
2
=
f. (a – b)
2
=
2) Fill in the blanks.
a. x
2
+ 10x + ____ = (x + 5)
2
b. x
2
– 8x + ____ = (x – 4)
2
c. x
2
+ 6x + 9 = ( x + ____ )
2
d. x
2
– 12x + 36 = ( x – ____ )
2
e. x
2
+ 18x + ____ = ( ____ + ____ )
2
Pre-AP Algebra 2 Name: _______________________
Lesson #3-4: Pairwork
Basic Factoring Practice
1) Fill in the missing number to make the expression into a perfect square trinomial.
a. x
2
+ 8x + ____ = (x + 4)
2
c. x
2
+ 12x + ____ = ( ____ + ____ )
2
b. x
2
– 4x + ____ = (x – 2)
2
d. x
2
– 10x + ____ = ( ____ – ____ )
2
2) For each parabola, first find the vertex by using x = -b/2a. Then, convert the function into
vertex form by completing the square. Do you get the same vertex in its new form?
a.
b.
3) Complete the square to convert the standard form quadratic function into vertex form.
a.
y = 3x
2
+ 4x + 2
b.
Pre-AP Algebra 2 Name: _______________________
Lesson #3-4: Homework
HW #3-4: Converting to Vertex Form
Check for Understanding
Can you complete these problems correctly by yourself
1) Complete the square to convert the standard form quadratic function into vertex form. Then
find the vertex and the x-intercepts.
a.
b.
f (x) = 2x
2
+ 9x
c.
y = 5x
2
- 4x +1
d.
e.
Pre-AP Algebra 2 Name: _______________________
Lesson #3-4: Homework
Spiral
What do you remember from Algebra 1and our previous units? (these are skills we will need
in this unit) Work on a separate sheet a paper
Given
1. Find the vertex using
2. Transform to intercept form by factoring
3. Transform to vertex form by completing the square
4. Graph and label the vertex, the
x-intercepts, the axis of symmetry,
and the y-intercept.
Use the graph to find the following
5.
6.
7. What value(s) of x make the following true
a.
b.
c.
d.
e.
f.
g.
h.
i.
