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Lesson 9.3B: From Vertex to General Form
Name ___________________________________________
Date __________
Hour __________
 Example 1: Simplify each expression by combining like terms.
a.) x 2  x  x  1  _______________
b.) x 2  9 x  9 x  81  _______________
You now know two forms of a quadratic equation:
vertex form: y  a( x  h)2  k
and
general form: y  ax 2  bx  c
In this lesson, you will learn how to convert an equation from the vertex form to the general form.
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Investigation 9.3B – “Sneaky Squares”
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A.) There are many different, yet equivalent, expressions for a number.
For example, 7 is the same as 3 + 4 and 5 + 2.
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3
7
This diagram shows how to express 72 as (3 + 4)2.
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Notice that 72 = ____, (3 + 4)2 = ____, and ____ + ____ + ____ + ____ = ____
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B.) 7 can also be expressed in different ways using subtraction.
For example, 7 is the same as 10 – 3 and 9 – 2.
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-3
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This diagram shows how to express 72 as (10 – 3)2.
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Notice that 7 = ____, (10 – 3) = ____, and ____ + ____ + ____ + ____ = ____
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2
-3
You can make the same type of rectangle diagram to square an expression involving variables.
C.) For each quadratic equation written in vertex form, describe the transformation, name the vertex,
and convert the quadratic equation from vertex form to standard form.
ii.) y = (x – 3)2
i.) y = (x + 5)2
Description:
iii.) y = (x + 11)2
Description:
Description:
Vertex: ( ___, ___ )
Vertex: ( ___, ___ )
Vertex:
( ___, ___ )
(x + 5)2 = _____________
(x – 3)2 = _____________
(x + 11)2 = _____________
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Lesson 9.3B: From Vertex to General Form
D.) For each quadratic equation written in general form, convert the quadratic equation to vertex form, describe
the transformation, and then name the vertex.
i.) x2 + 6x + 9 = __________
ii.) x2 – 10x + 25 = __________
iii.) x2 – 12x + 36 = __________
Description:
Description:
Description:
Vertex: ( ___, ___ )
Vertex: ( ___, ___ )
Vertex: ( ___, ___ )
E.) Use your results from D.) that are written in vertex form to solve each new equation symbolically.
i.)
x2 + 6x + 9 = 49
_________ = 49
ii.)
x2 – 10x + 25 = 81
___________ = 81
Numbers like 49 are called perfect squares because they are the squares of integers, in this case 7 or –7. The
trinomial x2 + 6x + 9 is the square of x + 3. So it is also called a perfect square.
F.) Which of these trinomials are perfect squares?
i.) x2 + 14x + 49
ii.) x2 – 18x + 81
iii.) x2 + 20x + 25
iv.) x2 – 12x – 36
G.) Explain how you can recognize a perfect-square trinomial when the coefficient of x2 is 1. What is the
connection between the middle term and the last term?
 Example 2: Convert the quadratic equation from vertex form to general form.
Rewrite y  2( x  3) 2  5 in the general form, y  ax 2 bx  c .
ASSIGNMENT: ______________________________________________________
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