Mhs, Ocdsb Mpm2d - Obtaining Vertex Form By Completing The Square/solving A Quadratic Equation Using Vertex Form Worksheet - Mathematics Department
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1
2MHS, OCDSB
MPM2D
Mathematics Department
Obtaining Vertex Form by Completing the Square
NAME:___________________
2
(
)
You have already been introduced to Vertex Form (
and you have learned several
y a x h
=
−
+
k
)
important reasons for using it. You learned how to use it to identify the Axis of Symmetry, the Vertex,
Direction of Opening, and the Number of Zeros. You also learned how to use it to easily sketch a
2
quadratic in Vertex Form by applying transformations to the parent curve (y = x
).
Today you will learn how to algebraically put a quadratic in Vertex Form. In addition you will also
learn how to solve a quadratic equation (factorable or non-factorable) by first putting the quadratic in
Vertex Form.
The Method of Completing the Square:
1. Group the x terms
2
2. Factor out the coefficient of x
, this includes –1
3. Complete the square inside the bracket by adding and subtracting the required value – Make a
Perfect Square Trinomial
4. Remove from the bracket the number not required to complete the square (the –‘ve number)
5. Rewrite as a perfect square and simplify
Ex 1)
2
y
=
5
x
+
20
x
+
3
(
)
2
1) Group the x terms
=
5
x
+
20
x
+
3
(
)
2
2
2
=
5
x
+
4
x
+
3
2) Factor the coefficient from the x
term(we must have a +’ve coefficient of the x
term)
(
)
2
=
5
x
+
4
x
+ −
4 4
+
3
3) make a Perfect Square Trinomial - The key question will be, how did you get the +/-4?
(
)
2
=
5
x
+
4
x
+
4
−
20 3
+
4) remove the number not needed for the Perfect Square Trinomial
2
(
)
=
5
x
+
2
−
17
5) rewrite as a perfect Square (factor) and simplify
Note: How did we get the +/-4 above?
We take half of the x coefficient and square it. This is the
value we add and subtract.
Ex 2)
2
y
2
x
20
x
2
= −
+
−
(
)
2
2
20
2
= −
x
+
x
−
(
)
2
= −
2
x
−
10
x
−
2
(
)
2
= −
2
x
−
10
x
+
25 25
−
−
2
(
)
2
= −
2
x
−
10
x
+
25
+
50 2
−
2
(
)
2
x
5
48
= −
−
+
Exercise
1. Put the following in Vertex Form and then find the Max or Min point.
2
2
2
a) y = -2x
+ 12x – 17
b) y = 3x
+ 90x + 50
c) y = -7x
+ 14x – 3
Completing the Square-1.doc
Page 1 of 2
May-3-09
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