MPM 2DI Unit 3 - Vertex Form Test Re-Write PDF
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This document contains a past paper on quadratic relations from a secondary school math examination. It includes problems about sketching quadratic relations, stating key features, and describing transformations using vertex form and completing the square, with associated questions.
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MPM 2DI solutions Name: ___________________ Unit 3 – Vertex Form Test Re-Write 3.8 & 3.9 – Sketching Using Vertex Form & Describing T...
MPM 2DI solutions Name: ___________________ Unit 3 – Vertex Form Test Re-Write 3.8 & 3.9 – Sketching Using Vertex Form & Describing Transformations 1. State the key features and sketch the following quadratic relations. State the transformations of each relation. ① ② ③ a) ! = −(% − 2)! + 9 Vertex: (2,9) w __________________ I D of O: down w __________________ 9 __ w Axis of Sym: __________________ x 2 9 = Max/Min? 9 ~ __________________ max of Step Pattern: 1,3,5 __________________ ~ ①vertical _________________________________ reflection across x-axis v ② _________________________________ horizontal shift zunik right I ③ vertical shift 9 units ~ _________________________________ up _________________________________ _________________________________ _________________________________ ⑥ ② B b) ! = 2(# + 7)2 − 4 Vertex: (-7, 4) ~ __________________ - w - D of O: __________________ U 9__ Axis of Sym: 7 ~ __________________ x = - 9 4 Max/Min? __________________ min of - Step Pattern: 2,6,10 ~ __________________ ①Vertical by a factor of2 _________________________________ stretch ~ _________________________________ ③ Horizontal shut 7mil left ~ _________________________________ ③ Vertical shift 4 mit daun _________________________________ _________________________________ _________________________________ MPM 2DI 3.10 – Completing the Square 2. Complete the square of the following quadratic relation and state the quadratic relation in vertex form. State the vertex. - ! = 2% ! − 4% + 5 y 2(x2 = - xx) 5 + = y 2(x2 2x 1 1 = 5 - + - + 1 = 6 __ 1 25 y 2(x2 2x - + = - + 6 y z(X = - 1)" 3 + w -: Vertex is (1,3) 3.11 – Changing Forms 3. Write both of the following quadratic relations in standard form. a) ! = 3(% + 1)! − 2 b) ! = 2(% + 1)(2% − 2) y 2(2x2 2x 2x z) y 3(x x(x 1) 2- - = + = - - + + ~ y 2(2x2 z) 6 2) 2- __ y 3(x 2x + - = = + - 6 ~ y 3x +6x 6 2 y 4x2 4 = = - - + +6x 4 y 3x = + Spicy Vertex Form 4. Given the following transformations, state the quadratic relation that satisfies these transformations. Vertical reflection across the x-axis 2 Vertical stretch by a factor of 4 Horizontal shift 5 units to the right z Vertical shift 2 units up y 5- 4x Quadratic relation: ____________________________ = - - __ 14
