Grade 10 Academic (MPM2D) Unit 4: Quadratic Relations The Quadratic Relation (Vertex Form) - Translations Mr. Choi © 2017 E. Choi – MPM2D - All Rights Reserved

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 © 2017 E. Choi – MPM2D - All Rights Reserved

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 © 2017 E. Choi – MPM2D - All Rights Reserved

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 © 2017 E. Choi – MPM2D - All Rights Reserved

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 © 2017 E. Choi – MPM2D - All Rights Reserved

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 © 2017 E. Choi – MPM2D - All Rights Reserved

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 © 2017 E. Choi – MPM2D - All Rights Reserved

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 © 2017 E. Choi – MPM2D - All Rights Reserved

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

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 © 2017 E. Choi – MPM2D - All Rights Reserved

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

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 © 2017 E. Choi – MPM2D - All Rights Reserved

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 © 2017 E. Choi – MPM2D - All Rights Reserved

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

End of lesson Quadratic Relations (Vertex Form): Translations © 2017 E. Choi – MPM2D - All Rights Reserved