Math 160 Notes Packet #6 Quadratic Functions - Prof. Beydler Page 2
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6Notes Packet #6
Math 160
Page 2 of 6
Ex 2.
2
Express �� ( �� ) = −2��
+ 12�� − 7 in standard form (by completing the square).
2
Let’s complete the square to get the vertex of a general quadratic function �� ( �� ) = ����
+ ���� + ��.
��
2
�� ( �� ) = �� (��
+
��) + ��
��
2
2
��
��
��
2
= �� (��
+
�� +
) + �� − �� (
)
2
2
��
4��
4��
2
2
��
��
= �� (�� +
)
+ �� −
2��
4��
2
��
��
So, the vertex is at (−
, �� −
).
2��
4��
��
Now we have a shortcut formula for finding the ��-value of the vertex: �� = −
����
Ex 3.
2
Let �� ( �� ) = −2��
+ 4�� − 5. Find the vertex of ��.
Find the maximum or minimum value of ��. State whether it is a maximum or minimum value.
What is the range of ��? ___________
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