1. Grade 10 Academic (MPM2D) Unit 4: Quadratic Relations The Quadratic Relation (Vertex Form) - Translations
Mr. Choi
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2. Quadratic Relations
A quadratic relationship is modeled by when this relationship is graphed; the graph of a quadratic relationship is called a parabola.
Vertex form of Quadratic Relations
The expression defines a quadratic relation called the vertex form with a horizontal translation of p units and vertical translation of q units.
The vertex of the quadratic relation is (p, q) and axis of symmetry is at x = p.
A quadratic relation in vertex form can be converted to standard form by expanding and collecting like terms.
Quadratic Relations (Vertex Form): Translations
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3. Quadratic Relations (Vertex Form)
The expression defines a quadratic relation called the vertex form with a horizontal translation of p units and vertical translation of q units.
x – intercepts
y – intercepts
Quadratic Relations (Vertex Form): Translations
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4. Quadratic Relations (Basic Points)
The basic points of a Quadratic Relation (Parabola) x y -3 9 -2 4 -1 1 2 3
Main focus
(11, 13, 15, …) pattern
Quadratic Relations (Vertex Form): Translations
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5. Example 1: Parabola with Vertical Translation (Method 1)
Given the quadratic relation, determine the x – intercepts , y – intercept, direction of opening, axis of symmetry and the vertex. Determine a mapping rule and a sketch of the relation on the given grid. Describe the translation.
This is Method 1!!
Quadratic Relations (Vertex Form): Translations
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6. Example 1: Parabola with Vertical Translation (Method 2)
Given the quadratic relation, determine the x – intercepts , y – intercept, direction of opening, axis of symmetry and the vertex. Determine a mapping rule and a sketch of the relation on the given grid. Describe the translation.
Down 4 units
(x , y) x y -2 4 -1 1 2
(x , y)  (x , y – 4) x y
y - 4 -2 4 -1 1 2 -2 -1 1 2 -3 -4
Mapping Rule:
Parabola moves down 4 units
Quadratic Relations (Vertex Form): Translations
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7. Example 1: Parabola with Vertical Translation (Method 1)
Given the quadratic relation, determine the x – intercepts , y – intercept, direction of opening, axis of symmetry and the vertex. Determine a mapping rule and a sketch of the relation on the given grid. Describe the translation.
This is Method 1!!
You only used the axis of symmetry and the vertex to draw the parabola!!
Quadratic Relations (Vertex Form): Translations
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8. Example 1: Parabola with Vertical Translation (Method 2)
Given the quadratic relation, determine the x – intercepts , y – intercept, direction of opening, axis of symmetry and the vertex. Determine a mapping rule and a sketch of the relation on the given grid. Describe the translation.
Up 2 units
(x , y) x y -2 4 -1 1 2
(x , y)  (x , y + 2) x y
y + 2 -2 4 -1 1 2 -2 -1 1 2 6 3 2
Mapping Rule:
Parabola moves up 2 units
Quadratic Relations (Vertex Form): Translations
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9. Example 2: Parabola with Horizontal Translation (Method 1)
Given the quadratic relation, determine the x – intercepts , y – intercept, direction of opening, axis of symmetry and the vertex. Determine a mapping rule and a sketch of the relation on the given grid. Describe the translation.
This is Method 1!!
Quadratic Relations (Vertex Form): Translations
© 2017 E. Choi – MPM2D - All Rights Reserved

10. Example 2: Parabola with Horizontal Translation (Method 2)
Given the quadratic relation, determine the x – intercepts , y – intercept, direction of opening, axis of symmetry and the vertex. Determine a mapping rule and a sketch of the relation on the given grid. Describe the translation.
Right 3 units
(x , y) x y -2 4 -1 1 2
(x , y)  (x + 3 , y) x y
x + 3 -2 4 -1 1 2 1 2 3 4 5 4 1
Mapping Rule:
Parabola moves right 3 units
Quadratic Relations (Vertex Form): Translations
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11. Example 2: Parabola with Horizontal Translation (Method 1)
Given the quadratic relation, determine the x – intercepts , y – intercept, direction of opening, axis of symmetry and the vertex. Determine a mapping rule and a sketch of the relation on the given grid. Describe the translation.
This is Method 1!!
Quadratic Relations (Vertex Form): Translations
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12. Example 2: Parabola with Horizontal Translation (Method 2)
Given the quadratic relation, determine the x – intercepts , y – intercept, direction of opening, axis of symmetry and the vertex. Determine a mapping rule and a sketch of the relation on the given grid. Describe the translation.
Left 2 units
(x , y) x y -2 4 -1 1 2
(x , y)  (x - 2 , y) x y
x - 2 -2 4 -1 1 2 -4 -3 -2 -1 4 1
Mapping Rule:
Parabola moves left 2 units
Quadratic Relations (Vertex Form): Translations
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13. Example 3: Parabola with Translations (Method 2)
Given the quadratic relation, determine a mapping rule and a sketch of the relation on the given grid. Describe the translation.
Left 3 units
Down 2 units
(x , y)  (x - 3 , y - 2) x y
x - 3
y - 2 -2 4 -1 1 2
(x , y) x y -2 4 -1 1 2
Mapping Rule: -5 -4 -3 -2 -1 2 -1 -2
Parabola moves left 3 units, down 2 units.
x-intercepts:
y-intercept:
Quadratic Relations (Vertex Form): Translations
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14. Homework
Work sheet: Quadratic Relations in Vertex form (Translations) Text: Check the website for updates
Quadratic Relations (Vertex Form): Translations
© 2017 E. Choi – MPM2D - All Rights Reserved

15. End of lesson Quadratic Relations (Vertex Form): Translations
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