Converting From General To Vertex Form Page 4
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1
2
3
4��
When �� ≠ ��:
�� = −
to find the ��-coordinate of the vertex. Then plug that value back into the
Use
����
equation to find the ��-coordinate of the vertex. What you have found is ( ℎ, �� ) . Lastly, identify the value for
��, and put the equation into vertex form. For #5 and #6, also find the axis of symmetry, max/min, domain
and range.
2
�� = − ��
+ 2�� + 5
�� =___________
5.
vertex:__________________
opens:______________
vertex form:______________________________
axis of sym:__________
max or min:______________
domain: __________________
range:____________________
2
�� = 2��
+ 8�� + 15
�� =___________
6.
vertex:__________________
opens:______________
vertex form:______________________________
axis of sym:__________
max or min:______________
domain: __________________
range:____________________
2
�� = − 4��
− 8�� + 9
�� =___________
7.
vertex:__________________
opens:______________
vertex form:______________________________
2
�� = 3��
+ 6�� − 7
�� =___________
8.
vertex:__________________
opens:______________
vertex form:______________________________
1. �� = ( �� + 2 )
2
− 3; vertex: ( −2, −3 ) ; axis of symmetry: �� = − 2; min value: − 3; domain: ( − ∞, ∞ ) ; range: [ − 3, ∞ )
2
2. �� = ( �� + 3 )
− 2; vertex: ( −3, −2 ) ; axis of symmetry: �� = − 3; min value: − 2; domain: ( − ∞, ∞ ) ; range: [ − 2, ∞ )
3. �� = ( �� − 1 )
2
− 2; vertex: ( 1, −2 ) ; axis of symmetry: �� = 1; min value: − 2; domain: ( − ∞, ∞ ) ; range: [ − 2, ∞ )
2
4. �� = ( �� − 4 )
− 4; vertex: ( 4, −4 ) ; axis of symmetry: �� = 4; min value: − 4; domain: ( − ∞, ∞ ) ; range: [ − 4, ∞ )
2
5. �� = − ( �� − 1 )
+ 6; vertex: ( 1, 6 ) ; axis of symmetry: �� = 1; max value: 6; domain: ( − ∞, ∞ ) ; range: ( − ∞, 6 ]
2
6. �� = 2 ( �� + 2 )
+ 7; vertex: ( −2, 7 ) ; axis of symmetry: �� = −2; min value: 7; domain: ( − ∞, ∞ ) ; range: [ 7, ∞ )
2
2
7. �� = −4 ( �� + 1 )
+ 13; vertex: ( −1, 13 )
8. �� = 3 ( �� + 1 )
− 10; vertex: ( −1, −10 )
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